Optional Science Book Class 10

UNIT

1 FORCE

Archimedes of Syracuse (287 BC–212 BC) was a Greek mathematician, physicist,

engineer, inventor and astronomer. He is considered as one of the most eminent scientists
and mathematicians of the classical era. He established strong foundations in the field of
mathematics, physics, particularly in statics, hydrostatics and also explained the principle
of the lever. The concept of "center of mass", in the form of the center of gravity, was first
introduced by him.

Key terms and terminologies of the unit

1. Force: Force is defined as the push or pull on a body, which changes or tends
to change the state of rest or uniform motion of a body in a straight line. It is a
vector quantity.

2. Scalar quantity: A quantity which has only magnitude is called a scalar quantity.

3. Vector quantity: A quantity which has both magnitude and direction is called a
vector quantity.

4. Centripetal force: The force on a body moving in a circular path, which is
directed toward the center, is called centripetal force.

5. Centripetal acceleration: The acceleration of a body in circular motion is called
centripetal acceleration.

6. Centrifugal force: The pseudo force that balances the centripetal force in uniform
circular motion is called centrifugal force.

7. Center of gravity: The center of gravity of a body is the point where the whole
weight of the body is supposed to act on the body.

8. Gravitational field: The region where a mass experiences a force due to
gravitational force is called gravitational field.

9. Gravitational field intensity: The gravitational field intensity at a point inside
the gravitational field is defined as the gravitational force experienced by a unit
mass placed at that point.

10. Escape velocity: The velocity of a projected body in space necessary to leave the
gravitational field of a planet or satellite is called escape velocity.

PHYSICS 0Optional Science - 10 1

Introduction

We use forces all the time. As we sit on a chair, a downward force is applied on the chair due
to the earth's pull on us. Forces are used in our everyday actions like pushing, pulling, lifting,
walking, pressing. We apply force on the ground while pressing it and while walking. Force
is used when we twist a wet cloth to squeeze out water. Force is defined as the push or pull
on a body, which changes or tends to change the state of rest or uniform motion of a body in
a straight line. It is a vector quantity.

In class nine, you learnt about contact forces and non-contact forces. Friction, upthrust, surface
tension, air resistance are contact forces. Gravitational force, magnetic force and electrostatic
force are non-contact force. In this unit, we look at vectors and scalars, their representation,
addition and subtraction. We will also learn about centripetal force and centrifugal force,
gravitational field intensity, escape velocity and stability of a body.

Physical Quantities

A variety of quantities are used to describe the physical world. For example, distance,
displacement, speed, velocity, acceleration, mass, momentum, energy, work, power. We see
that some of these quantities and processes depend on the direction in which they occur, and
there are some quantities that do not depend on direction. All such quantities can be divided
into two categories. They are scalars and vectors.

Physical Quantities

Scalar: A scalar is described by a Vector: A vector is described by
number and unit. e.g. mass (m) = 5 kg, its magnitude and direction. e.g.
temperature (T) = 273 K, etc. displacement (s) = 10 m east

Scalar quantities

There are some quantities in our world that do not depend on direction. A quantity which has
only magnitude is called a scalar quantity. It is denoted by a number and unit. For example,
length, mass, time, speed, work, energy, temperature. Comparison of scalar quantities depends
only on the comparison of their magnitude. Scalars of the same kind can be added, subtracted,
multiplied or divided by ordinary laws.

Vector quantities

Some physical quantities are described by a magnitude with directions. For example, a
displacement of 1 km to the east, a force of 100N towards centre of the earth, etc. In first
example, 1km denotes 'magnitude' and east denotes 'direction' of displacement. Similarly, in
second example 100 N denotes 'magnitude' and towards centre of the earth denotes 'direction'
of force. Thus, a quantity that has magnitude as well as direction is called a vector quantity.
For example, displacement, velocity, acceleration, force, weight, momentum.

Memory Plus

The necessary condition for a physical quantity to be a vector is that the quantity must
have magnitude and direction.

2 Optional Science - 10

PHYSICS

Know the Reason

Mass is a scalar quantity, but weight is a vector quantity, why?

Mass is described by magnitude and unit. But weight is a force towards the center of a
planet or satellite. Weight has both magnitude and direction. So mass is a scalar quantity,
but weight is a vector quantity.

Comparison of vectors depends on both magnitude and direction. We cannot add, subtract
and multiply vectors using general algebraic rules. There are special rules to simplify vectors.
They are given a special notation while representing them.

Vector notation

While writing a vector by hand, we use the symbol of a physical quantity with an arrow on
top. For example, acceleration is written as →a . When printed, it is in bold print as a.
The magnitude of a vector is denoted either by the symbol |→a | or by the symbol of the vector

written with the regular type as 'a'.

Graphical representation of vector quantities North

Graphically vector quantities are

represented by a scaled vector diagram. West 5 -•..4,11-3---+-2--1--1--- Origin
The directed line in a vector diagram
represents a vector quantit y. A scaled (' ------East
vector diagram is shown in the given AO
OA represents displacement of 45m due west '

figure. South

From the given figures, to represent a North
vector we follow following steps:

1. The scale is listed. X

2. A line with an arrow is drawn in a 5
specified direction.
4 A
3. The magnitude and direction of the 3
vector are clearly labelled.
2
1

In the first figure, the vector represents a West 30o East
displacement of 45m towards the west on O

a scale of 1cm= 10m. → South

In the second figure, the OA represents a force of 5 N in the direction of 30° to x-axis on a scale

of 1 cm= 1N. The length of the line gives the magnitude while the arrow head gives the

direction.

Memory Plus

In a vector notation, → , point O is called the initial point of the vector, and point A is

OA

called the terminal point. The arrowed end of the vector is called the tip, and the other

end is called the tail.

Optional Science - 10 3

PHYSICS

Differences between scalar quantities and vector quantities

Scalar Quantities Vector Quantities

They are expressed in magnitude only. They are expressed in magnitude as well as
direction.

They are denoted by a normal letter like They are denoted by a letter with an arrow
head on its top like acceleration,' →a '.
time, 't'.

Their addition, subtraction and multiplication Their addition, subtraction and multiplication

is possible using general algebraic rules. is not possible using general algebraic rules.

They cannot be easily plotted on a graph They can be easily plotted on a graph paper.
paper.

The sum of the scalars is always positive. The sum of the vectors can be positive,
negative or zero.

Scalar addition

Mass is a scalar quantity. Can you find the resultant of 2 kg and 3 kg masses in your hand? It is
a simple problem for you. Just add each of them to find the resultant. So simple algebraic rules
are used to add scalars. For example, suppose the mass of a boy is 60 kg and that of another
boy is 50 kg. When they sit on a bench, the resultant mass on the bench is given by simple
addition i.e. 60 kg + 50 kg = 110 kg.

Vector addition

The process of obtaining the resultant or sum of the vectors is called addition or composition

of vectors. Vectors cannot be added using the simple rules of algebra applicable to scalars. For

example, we walk first north 20 m d(si1s)palnacdemtheennte. aTshta1t0ism, →s(s≠2)s.1+Ws2e. cannot add the magnitude
of →s1 and →s2 to obtain the resultant

Graphical and analytical methods are commonly used for vector addition.

Graphical addition of vectors or geometric method

The graphical method is a convenient way to describe the rules for adding vectors. Vector
addition can be done easily by this method. This method is also known as the head-to-tail
method. In this method, the vectors are drawn to scale and added by drawing the resultant.

Adding vectors in one dimension
Two collinear vectors →a and →b can have different possible direction with respect to each other.

Case1: When the vectors are parallel →a + →b = →R
When the vectors →a and →b are parallel, the magnitude of

their resultant is equal to the sum of the magnitude of both

the vectors. It acts in the same direction of the components. . - -scale: 1 division = 100m b= 400m,E +N
a= 200m,E
In vector form, the resultant is given by, WE
→R = →a + →b S

In the given figure, →a and →b represent two segments of a child's walk. They are added by
placing the tail of one vector at the head of the other vector. Here the resultant →R is the third
vector drawn from the tail of the first vector to the head of the second vector, →R = 600m, E.

04 Optional Science - 10

PHYSICS

Example:

A man walks 54.5m east, then another 30m in the same direction. Find his resultant
displacement.

Solution: 54.5m,E + 30m,E
Let, →a = 54.5m East, →b = 30m East

Resultant is given by 84.5m,E
→R = →a + →b = 84.5 m,E

Case2: When the vectors are anti-parallel

When the vectors are anti-parallel, the magnitude of their resultant is equal to the difference

of magnitude of both the vectors. It acts in the same direction of the vector having a greater

magnitude. In vector form, the resultant is given by, →a - →b = →
→R = →a + (-→b ) R

In the given figure, a child returns after moving 200m east and a= 200m,E N
walks 400m west. In this case also the vectors are added head to
tail, and the resultant is drawn from the tail of the first vector to b= 400m,W WE
the head of the last vector. The resultant is equal to 200 m west. S

Adding vectors in two dimension R= 200m,W

We can add non-collinear vectors by the triangle method, parallelogram method and polygon
method.

Triangle method

In the triangle method, if two vectors are there: -I _J→a→b

1. The tail of the second vector →b is placed at the tip of the first vector →a . d→R →+b head to tail

2. Tail of the first vector→a is joined with the tip of the second →b. Which →=a
→ of the two vectors. That is, →R = →a +
gives →b .
the resultant R
→
3. Length of R gives the magnitude of the resultant vector and its angle gives the direction

of the vector.

Know the Reason

The graphical method for adding vectors is also called 'head-to-tail method', why?

In the graphical method of adding vectors, vectors can be added by arranging them in such
a way that the tail of the second vector is placed at the head of the first vector and so on. The
resultant vector, →R is the vector drawn from the tail of the first vector to the tip of the last
vector. So the graphical method for adding vectors is also called the 'head-to-tail method'.

Example: scale: 1 division = 10 m B= 55m,90o
R= 110m,30o
→A represents the displacement of a student 95m east and →B
represents the displacement of 55m north. These two vectors A= 110m,0o
are added by placing the tail of one vector at the head of the
other vector. The resultant is the vector drawn from the tail of
the first vector to the head of the second vector.

Optional Science - 10 5

PHYSICS

The scale used is 10m/division. Thus the resultant is given by
→R = Number of divisions × scale factor = 11divisions × 10 m/ division = 110 m,30o.

Here, 30o is the angle made by the resultant with vector →A. It is measured with the help of a

protactor.

Example: I→a b→ b→

Draw a diagram to show the resultant of the given vectors,→a and →b by the L YR→
triangle method. →a

When angle between two vectors is 90°

In such cases, there is formation of a right angled triangle. P² +Q²= 5 units Q

We can find →the resultant by using the Pythagoras's = →R →Q
theorem. Let, PQ →represents a displacement of 4m from P
R² R
to Q towards east.QR represents a displacement of 3m from
Q to R towards north as shown in the given figure. PQR is P →P
a right angled triangle.

Magnitud→e of the resultant: The magnitude of the

resultant PR can be obtained by Pythagoras theorem
as

PR² = PQ² + QR² (since, h² = p² + b²)

Here, PQ, QR and PR represent the magnitude of the corr→esponding vectors.

Direction of the resultant: The direction of the resultant PR can be obtained by

tanθ = QR (since, tan θ = p )
PQ b
Here, θ gives the direction of the resultant displacement from the initial point P to the

final point R.

Parallelogram method A ii
When two vectors →A and →B are to be added, then we
A
can use the parallelogram method. In this method,

tails of the two vectors are joined to a common point

and the remaining sides are sketched to determine

the diagonal. The diagonal through the common
point of the two vectors gives the resultant, →R .

Example:
Draw a diagram to show the resultant of vectors →a and →b by the parallelogram method.

→a

→b →b
R→

→b

→a →a

06 Optional Science - 10

PHYSICS

Polygon method →D

If a number of vectors are there, a geometric construction in the R→= A→+B→+C→+D→ →C
form of a polygon can be made to add them: →B

1. Vectors are drawn continuously “tip-to-tail”. →A
2. The resultant is drawn from the origin of →A to the end of

the last vector
The length of →R is measured with the help of a scale, and a
protector is used to find its angle. Use the scale factor to convert
the length to the actual magnitude.

The polygon law of vector addition states that if a number of vectors acting simultaneously at
a point are represented in magnitude and direction by the sides of a polygon taken in the same
order, then the closing side of the polygon taken in opposite order represents the resultant in
magnitude and direction.

Things to remember in the graphical method of vector addition:

1. The length of each vector must correspond to the magnitude of the vector according to
the scale chosen while plotting them. For example, 1cm=1 m.

2. When the vectors are shifted while joining the tip to the tail, the direction of each vector
must be parallel to itself.

3. The vectors in the sum must represent the same physical quantity.

Subtraction of vectors

The concept of vector subtraction is derived from the →B
definition of negative vector. The operation →A—→B is
defined as the vector sum →A + (—→B ). That is, if we are →A
given two vectors →A and →B then to subtract →B from →A
we need to →A—→B —→B
1. determine —→B from →B .
2. add vector—→B to vector →A.

The geometric construction for subtracting two vectors
is shown in the given figure.

Example:
Draw a diagram to subtract the given vector →p from →q .

→p →p →p

— = + = →p —→q —→q

→q —→q

PHYSICS 0Optional Science - 10 7

Centripetal and centrifugal force

Centripetal force

Activity: Whirling a soft ball

1. Take a 1.5 meter long string and tie a soft If the string is released when
ball at one end. ball is here, then it goes straight
towards A not towards B.
2. Hold another end of the string and whirl
that ball over your head. Does that ball A
move in a circular path? Do you need to
pull the string inward in order to keep B I \
the ball in circular motion? I
I
I I
I I
I
I I

I
I
I

\

3. Release the string from your hand and Side view Top view
let the ball fly off. Does that ball follow
a straight path after releasing the string
from your hand?

While whirling a ball from a piece of string, we feel that our hand is being tugged
outward by the stone. We need to exert a force inward to keep the stone moving in a
circular path. If the string breaks, then the stone will move in a straight line tangential
to the original circle. It does not remain in that circular path.

According to the Newton's first law of motion, 'a body in motion continues its state of motion
in a straight line unless an unbalanced force acts on it'. But many things move in circles. Thus,
there must be a force on the bodies in a circular motion, which pulls them out of their straight
paths and makes them turn corners.The force on a body moving in a circular path, which is
directed toward the center, is called centripetal force.

Some examples of centripetal force

1. While whirling a ball in a circular path, the centripetal force is provided by the tension in the
string.

2. In satellite motion, the gravitational force between a planet and the satellite provides
the centripetal force needed.

3. When a car goes around a curve, the friction between the tires and road provides the
necessary centripetal force.

4. The electrostatic force of attraction between the electron and the nucleus provides the
centripetal force to the electrons revolving around the nucleus.

. ---- ~
.··~equ1red~ tnng . '-. )~
!; tension Centripetal force
)3. 4.
, ~--c-e--n-tr-ipetal

( T= ~v2 T :/: ' fo~-
- - - - - - atectron
\, ...·

1. 2.

8 Optional Science - 10

PHYSICS

Some characteristics of centripetal force
1. It is a real force.
2. Centripetal force is only involved in circular motion.
3. It is always directed towards the center of a circular path.
4. As the centripetal force is perpendicular to the direction of motion, work done by it is

zero.

Know the Reason

Centripetal force is a real force, give reason.
The centripetal force is provided by different agencies, like gravitational force,
electromagnetic interaction, nuclear interaction, frictional force, etc. So it is a real force.

Expression of centripetal force v= rω

The direction of a body moving with constant speed in a circular ram
track changes continuously. It means the body is in acceleration. r
The acceleration of a body in circular motion is called centripetal
acceleration. Its SI unit is m/s2. This acceleration is always directed
towards the center of the circular track.

Suppose an object of mass 'm' is moving in a circular path of

radius 'r' at constant speed. The magnitude of the centripetal

acceleration is given by;

a = v2
r

Since, v = rω, where, 'v' is the linear velocity and 'ω' is the angular velocity of the body.

∴ a = rω2

The centripetal force acting radially towards the center is given by

F= ma = mv2 = mrω2
r

Memory Plus

The rate of change of angular displacement is called angular velocity. It is denoted by 'ω'.
Its SI unit is radian per second (rad/s).
The centripetal force
1. increases with increasing mass of the object
2. increases with increasing speed of the object
3. decreases with increasing radius of the circular path

Direction of centripetal force and velocity in circular motion velocity is directed
tengential to the circle
In a circular motion, the centripetal force is directed inwards from the
object to the center of rotation along the radius vector. In such a motion, the v
tangent at any point on the circular path gives the direction of velocity. The
velocity of the object and centripetal force are perpendicular to one another. a
Force and acceleration
are directed towards
center of the circle.

Optional Science - 10 9

PHYSICS

Applications of centripetal force

1. Bending of a cyclist: A cyclist while going round a curve on a horizontal track has to
bend himself a little from his vertical position, in order to avoid overturning. When he
bends himself inward, then the component of the reaction of the road and the force of
friction combine together to provide him the necessary centripetal force for circular
motion.

2. Banking of roads: The phenomenon of raising the outer edge of a curved road above
the inner edge for necessary centripetal force to the vehicles to take a safer turn is called
banking of roads. The knowledge of centripetal force is used when designing roads
to prevent skidding on a curved road. The horizontal component of normal reaction
and the force of friction combine together to give the necessary centripetal force that is
needed to make the car go round the curve.

3. To find the orbital velocity of a setallite: The expression of centripetal force is used
to find the orbital velocity of a satellite around the earth. Earth's gravity provides the
inward force, which keeps the satellite in its orbit. To keep a satellite in an orbit, the
centripetal force is equal to the gravitational force between the satellite and the earth.
This gives the necessary tangential velocity 'v' of the satellite in a particular orbit.

Centrifugal force

Activity: Rotate a bucket with water in a vertical plane at a particular speed, so that
water does not pour. Do you observe that water does not pour? This is due to the balance
between the weight of the water and centrifugal force.

We feel an outward push at sharp turnings when the driver of a vehicle turns it. This is due
to the effect of the centrifugal force. It is actually not a force. It is the tendency of a body to
move in one direction, which causes a body turning around a center to move away from the
center. The pseudo force that balances the centripetal force in uniform circular motion is called
centrifugal force.

Memory Plus

The magnitude of the centrifugal force is the same as the centripetal force, but the

direction is along the radius and directed away from the center of the circle.

i.e., Magnitude of centripetal force = Magnitude of centrifugal force = mv2
r

Some examples of centrifugal force:
1. When a ball tied at one end of a string is whirled, the centrifugal force pulls the ball

away from the center of the circle.

2. Chemicals can be separated in a centrifuge by a centrifugal force.

3. On a moving merry-go-round, we feel our body being acted upon by a force. Actually
there is no force on the body.

4. Mud flying off the tires of a vehicle in motion,

10 Optional Science - 10

PHYSICS

Know the Reason

Centrifugal force is a fictitious force, give reason.
Centrifugal force does not arise due to either gravitational, or electrostatic or nuclear
interaction. It arises due to acceleration of a rotating frame. So centrifugal force is a
fictitious force.

Some characteristics of centrifugal force
1. It is a factitious force.
2. It is directed away from the center, along the radius.
3. It does not have an independent existence.
4. It is equal and opposite to the centripetal force, but it is not the reaction of the centripetal

force.

Applications of centrifugal force

1. The knowledge of centrifugal force allowed for the invention of the centrifuge, which
separates particles suspended in a fluid by spinning test tubes at high speed.

2. The dryer of a washing machine acts on the principle of the centrifugal force. The water
molecules from wet clothes are thrown outward due to the centrifugal force acting on
them.

3. In order to give a bulge to an earthen pot at its middle, the soft clay used to make such
pots is rotated on a wheel. The centrifugal force acting on the soil particles at the middle
is maximum.

Differences between centripetal force and centrifugal force

I- I Centripetal force I Centrifugal force -1

~ -
The force on a body moving in a The pseudo force that balances the
Meaning

circular path, which is directed centripetal force in uniform circular

toward the center, is called the motion is called centrifugal force.

centripetal force. -
Defined by Isaac Newton in 1684 AD.
Christiaan Huygens in 1659 AD.

Direction -
I_Nature It is a 'center-seeking' force, i.e., it It is a 'center-fleeing' force, i.e., it acts

acts along the radius and is directed along the radius and is directed away

towards the center of the circle. from the center of the circle -
I It is a real force. It is a fictitious force. J

Center of gravity

Have you ever seen a man carrying a ladder on his shoulder? How does he adjust the length
of the ladder on either sides of his shoulder to balance the ladder? He tries to find the point
where the whole weight of the ladder is supposed to act. He keeps that point of ladder over
his shoulder. That point is the center of gravity of the ladder. The center of gravity of a body is
the point where the whole weight of the body is supposed to act on the body.

Optional Science - 10 11

PHYSICS

We can completely describe the motion of any object through space in terms of the translation
of the center of gravity of the object from one place to another and the rotation of the object
about its center of gravity if it is free to rotate. In flight, both airplanes and rockets rotate about
their centers of gravity. A kite, on the other hand, rotates about the bridle point. But the trim of
a kite still depends on the location of the center of gravity relative to the bridle point, because
for every object the weight always acts through the center of gravity.

Locating center of gravity

The center of gravity can be located within or outside the body depending on the body’s
configuration and position. In case of a body with mass distributed uniformly throughout it,
the center of gravity (CG) can be determined simply by finding the geometrical center. But it is
a complicated procedure to find the center of gravity when the mass of a body is not uniformly
distributed throughout the object.

1. For regular and uniform objects

In the case of regular and uniform objects, the CD~. .·-_:J...'' ••
center of gravity is at the geometric center. If .,. .. I -:.•
the object has a line (or plane) of symmetry, the . !•
CG lies on the line of symmetry. In the given
diagrams, 'G' represents their center of gravity. fig: center of gravity of regular objects

2. For general shaped objects

In the case of a general shaped object, the center of gravity is determined by some
simple mechanical ways:

i. By finding the balancing point

In this method we just balance the object using a string or an edge, the point at which
the object is balanced is the center of gravity.

ii. By suspending objects:

Activity: To find the center of gravity of an irregular object

1. Drill a small hole at one end of the object and hang Hang from here

it up so that it can swing freely. Plumb-line

2. Hang a plumb-line (a piece of string with a weight
hanging from it) on the same suspension point.

3. When the object comes to rest, use a plumb-line to
draw a vertical line on it.

4. Drill another hole at a different location within

the object. Hang it again and repeat the above

procedure to draw another line on the object. Do center of gravity

you find a point of intersection of the two lines? fig:center of gravity of irregular objects

The point where the two lines cross is the center of gravity.This procedure works well

for irregularly shaped objects that are hard to balance.

Center of gravity and stability

Stability refers to the ability of a body to come back to its original equilibrium when it is
slightly displaced. The position of the center of gravity of an object affects its stability.

012 Optional Science - 10

PHYSICS

Conditions for stability: To make a body more stable

1. Lower its center of gravity:The lower the center of gravity (CG), the more stable an
object. A higher center of gravity increases the probability of the object toppling over.

2. Increase the area of base: In the case of a wider base, the center of gravity remains
inside its base and does not topple easily.

Real life applications

1. The luggage compartment of a tour bus is located at the bottom rather than on
the roof.

2. Extra passengers are not allowed on the upper deck of a bus.

3. Table fans, table lamps are designed with a larger heavy base.

4. The center of a building is lowered if much of the structure is below the ground.

5. A tall object with a narrow base, such as a bookcase, will have a high center of
gravity and thus only a small force applied towards the top of the object can
topple it over.

6. Racing cars are built low and broad.

Center of gravity and stability of a vehicle:

1. Empty vehicle can be unstable

The heaviest part of an empty vehicle is not at the center of the vehicle. It lies in the
engine compartment. The center of gravity is not well supported. The front axles bear
most of the weight. That’s why an empty vehicle can be unstable.

When a load as heavy as the engine is added in the vehicle, then the center of gravity
shifts somewhere around the front half of the cargo area. In such a condition, each axle
is supporting an equal amount of weight. The vehicle is stable.

If the cargo is heavier than the engine of the vehicle, then the center of gravity of the
whole load is towards the rear of the vehicle. The vehicle in not stable in this condition,
too.

2. Buses are built closer to the ground

Buses are shorter in height and built lower to the ground than trucks. This makes them
more stable as their center of gravity is lowered. However,a double-decker bus has a
higher center of gravity and presents a driving challenge.

Know the Reason

Buses are more stable than trucks, why?

As buses are built closer to the ground, the weight is distributed throughout the vehicle
body. The load of passengers is not likely to have a high center of gravity. The center of
gravity is well supported even in an empty bus. So the buses are more stable than trucks.

A Formula 1 car is very stable, and a large force must be applied to topple it, why?

To make a body more stable, we need to lower its center of gravity and increase the area
of its base. A Formula 1 car is also made with a wide base and low height. So a Formula 1
car is very stable, and a large force must be applied to topple it.

Optional Science - 10 13

PHYSICS

3. Vehicles that are too tall are unstable

When a load is added to a greater height, the center of gravity shifts towards the roof.
That is called a high center of gravity. On a level road, it is not a serious problem, but
on a banked road, the body of the vehicle tilts away from the high side of the bank. The
center of gravity is no longer over the center of support. It is away from the central line.
The vehicle is unstable. A vehicle carrying even a legal amount of weight can be unsafe
due to the center of gravity problem.

Gravitational field

A mass exerts force on another mass kept at a certain distance. This is due to the gravitational
field around a mass. The gravitational field of a material body is the space around the body
in which any other mass experiences a force of attraction. For example, the earth produces a
gravitational field around itself and then exerts force on the object inside that field. The region
where a mass experiences a force due to the gravitational force is called gravitational field.
The effect of the gravitational field decreases as the distance from the body is increased. This
distance depends on the mass of the body.

Gravitational field intensity

The gravitational field of a planet or satellite has a different magnitude at a different point. The
exact effect of the gravitational force at a point in the gravitational field is measured by
gravitational field intensity. The gravitational field intensity at a point inside the gravitational
field is defined as the gravitational force experienced by a unit mass placed at that point.

Memory Plus

Gravitational field intensity is a vector quantity and its direction is the same as that of
the gravitational force.

Let us consider a test mass of 'm' at a point 'P'. It is at a distance of 'r' from the center of the

planet having mass 'M' and radius 'R'. h

According to Newton's universal law of gravitation, the gravitational m
R
force is given by
rP
F = GMm
r2 M

Where 'G' is the universal gravitational constant whose value is equal
to 6.67×10-11 Nm2kg-2.

The gravitational force experienced by a unit mass at P is the

gravitational field intensity at that point. It is denoted by 'I' and given by

I = -mF == --GMmr2 m

... I= GM
r2

It is directed towards 'M'.

The SI unit of gravitational field intensity is Nkg-1 and CGS(centimeter-gram-second) unit is
dyneg-1.

14 Optional Science - 10

PHYSICS

A Special Case:

When r = R, i.e., the object is on the surface of a planet,

Gravitational field intensity, I= GM
R2

This means that the gravitational field intensity on the surface of a planet is equal to the value
of acceleration due to gravity, i.e., I= g.

For example, the gravitational field intensity on the earth

at the pole, IP = 9.83 Nkg–1
at the equator Ieq = 9.78 Nkg–1.

Memory Plus

The weight of a body of mass 'm' at a place where the gravitational field intensity is 'I'
is given by
W = Mass (m) × Gravitational field intensity (I)

Solved numerical

1. The mass of the moon is 7.2× 1022 kg and its radius is 1.7× 106 m. Find the gravitational
field intensity on its surface. What is the weight of a body of mass 100kg on its surface?
(G = 6.67 × 10-11 Nm2/kg2)

Solution:

Here, mass of the moon (M) = 7.2 × 1022kg

Radius of Earth (R) = 1.7× 106m

The gravitational field intensity (I) due to the moon of mass M and distance R from its

center is given by

I= GM
R2

Or I = 6.67 × 10–11 × 7.2 × 1022
1.7× 106 × 1.7× 106

Or I = 48.02 × 1011
2.89× 1012

Or I= 16.7
10

I = 1.67 N/kg

Therefore, the gravitational field intensity on the surface of the moon is 1.67 N/kg.

Now, the weight of a body of mass 100kg on its surface is given by

W = Mass× Gravitational field intensity

Or, W = 100× 1.67 = 167 N

Therefore, the weight of a body of mass 100kg at its surface is 167 N.

PHYSICS 0Optional Science - 10 15

Escape velocity

According to the old concept, “what goes up,

must come down”. But while thinking about

gravity, Isaac Newton developed the concept of

an orbit around the earth, in which a projected

object from the earth can revolve. He imagined a

cannon on top of a tall mountain. When we fire a

cannon, the ball travels horizontally for a short

way before falling to the ground. The next time Escape velocity

when we fire it at a faster speed, the ball travels

further before falling. As the earth is spherical, Orbital velocity
there must be a speed at which the ball would

keep travelling horizontally and falling towards the earth's surface but never actually hit it. If

the velocity of the projection is equal to the orbital velocity (i.e., 7.1 km/s), then it will go round

the earth in an orbit. Firing the cannon ball with even greater speeds results in elliptical orbits.

Memory Plus

Luna 1, launched as part of the Soviet Luna program in 1959, was the first man-made
object to attain escape velocity from Earth. It was the first spacecraft to reach the vicinity
of the earth's moon.

If an object is thrown upward from the earth's surface, its velocity decreases due to the
downward force of gravity. Such effect is within the earth's gravitational field. The height
which will be attained by an object like a rocket after being launched from the earth's surface
depends on the speed with which it is projected. The greater the speed, the greater the
height. For instance, imagine an experiment where a cannon shoots straight upward instead
of shooting sideways. Each time more gunpowder is added, the cannonball will travel to a
greater height and take longer to come back down. If an object is projected upward from the
earth's surface with such a high velocity that it can escape the gravitational pull of the earth,
then it does not return towards the earth. In such a condition, the object has sufficient initial
kinetic energy to overcome the earth's gravitational pull. The necessary velocity of a projected
body in space to leave the gravitational field of a planet or satellite is called escape velocity.

Expression for escape velocity

Suppose an object of mass ‘m’ is projected vertically upward from the earth’s surface. The
mass of the earth is ‘M’ and its radius is ‘R’.

For an object to escape from the earth’s gravitational pull, work has to be done against the
gravitational force. In such a condition, the initial kinetic energy of the object is due to the
work done against the gravitational force.

i.e. Kinetic energy = Work done against gravitational force
Or 12mve2 = Gravitational force × displacement

Where ve is the escape velocity. The displacement is equal to the distance between the center
of the earth and the projected object on the earth's surface, which is the radius of the earth, R.

16 Optional Science - 10

PHYSICS

Or 12mve2 = GMm × R
R2

Or ve2 = 2GM
R

FOr ve = 2GM
R

✓ -Or ve = 2 × GM × R
R
r -ve = 2gR
(since, g= GM )
R2

Substituting

Mass of the earth ‘M’ = 6×1024 kg

Radius of the earth ‘R’ = 6400 km = 6.4×106 m

F - -ve =
2GM = 2 × 6.67 × 10–11 × 6×1024
R 6.4×106

✓-Or 80.04× 1013—6
ve = 6.4

ve = 11,183.134 m/s ~ 11.2 km/s

The escape velocity of an object on the earth is 11.2 km/s or about 7 miles/s.

Factors which determine escape velocity

The expression to find the escape velocity on a planet or satellite is given by

ve = 2GM = 2gR
R

Where ‘M’ is the mass of the planet and ‘R’ the radius of the planet. Thus, escape velocity
depends upon

1. mass of a planet/satellite (M)

2. radius of the plant/ satellite (R)

Memory Plus

From the expression of escape velocity, the escape velocity is independent of the mass
of the body and direction of the projection. It depends on the mass and the radius of the
planet from which it is being projected.

The velocity of escape from the earth at its surface is about 7 miles (11.2 km) per sec,
or 25,000 miles per hr; from the moon’s surface it is 1.5 miles (2.4 km) per sec; and for
a body at the earth’s distance from the sun to escape from the sun’s gravitation, the
velocity must be 26 miles (41 km) per sec.

Trajectory of a body when it attains escape velocity

If an object attains escape velocity, but is not directed straight away from the planet, then it
will follow a curved path. Such a path is not a closed path like that of the moon to revolve
around the earth. It is an open curve. That is, a parabola or hyperbola.

PHYSICS 0Optional Science - 10 17

1. If an object attains escape velocity, then the shape of the trajectory will be a parabola,

whose focus is located at the center of the mass of the planet. An actual escape path is

called an escape orbit.

2. If the body has a velocity greater than the escape Hyperbola, v>ve
velocity, then its path will form a hyperbolic Parabola, v= ve

trajectory, and it will have an excess hyperbolic

velocity, equivalent to the extra energy the body Ellipse, Circle, Ellipse,
has. vc< v< ve v=vc v<vc

Without any other force except gravity, the speed at any
point in the trajectory will be equal to the escape velocity

at that point. In the solar system, a rocket that travels at

escape velocity from Earth will not travel to an infinite Circular velocity vc = 7.9 km/s
distance because it needs an even higher speed to escape Escape velocity ve= 11.2 km/s
the sun's gravity.

Answer writing skill I

1. What is the direction of the instantaneous velocity of a stone going around a circular
path?

The instantaneous velocity of a stone going around a circular path is tangential to the
circle.

2. Write the condition in which the gravitational field intensity is equal to the value of
acceleration due to gravity.

On the surface of a planet or satellite, the gravitational field intensity is equal to the
value of acceleration due to gravity.

3. What is the value of gravitational field intensity at pole and equator of the earth?

The gravitational field intensity at the pole, IP = 9.83 Nkg–1 and at the equator Ieq = 9.78
Nkg–1.

4. What are the two factors which affect escape velocity?

The escape velocity depends upon

1. mass of a planet/satellite (M)

2. radius of the plant/ satellite (R)

5. In which condition does the block shown in the given figure topple over? Give reason.

The block topples over in the second case. In the first figure, the A B
block is slightly above the table. Its center of gravity is inside the

base. The block's weight produces an anti-clockwise moment,

and the block falls back to its original position. In the second

figure, the block is tilted far enough. Its center of gravity is beyond the base. The block's

weight produces a clockwise moment and topples it over.

018 Optional Science - 10

PHYSICS

6. Draw a vector diagram for the displacement of 5m, 30o north of east.

Scale factor= 1m/cm

North

..-·X

5 ~.,•·
4A
3

2
1

West 30o East
O

South

7. Find the gravitational field intensity at a height of 3,600 km from the surface of the earth.
The radius of the earth is 6,400 km and its mass is 6 × 1024 kg.

Solution: Here, the mass of the earth (M) = 6 × 1024 kg

Radius of the earth (R)=6,400 km

Height from the earth surface (h) = 3,600 km

Distance from the center of the earth (r) = 6,400km+ 3,600 km = 10,000,000m = 107 m.

The gravitational field intensity at a distance of 'r' from the center of the earth is given by

I= GM
r2

Or I = 6.67 × 10–11 × 6 × 1024 = 40.02 × 1013
(107)2 1014

Or I= 40.02 = 4.002 N/kg
10
Therefore, the gravitational field intensity at a height of 3,600 km from the center of the

earth is 4.002 N/kg.

8. Show that the gravitational field intensity at a test point is inversely proportional to
-1
the square of its distance from a planet or satellite. i.e., I oc r2

Let us consider a test mass of 'm' at a point 'P'. It is at a distance h
of 'r' from the center of a planet having mass 'M' and radius 'R'.
m
According to Newton's universal law of gravitation, the R

gravitational force is given by rP

F = GMm M
r2
Where 'G' is the universal gravitational constant whose value is

equal to 6.67×10-11 Nm2kg-2.

The gravitational force experienced by a unit mass at P is the gravitational field intensity

at that point. It is denoted by 'I' and given by
GMm

I = F == r2 = GM
m m r2

Here 'G' is a constant and 'M' is also constant for a particular planet or satellite.

Hence, I oc 1
r2

PHYSICS 0Optional Science - 10 19

Exercise

1Step

1. Define

1. force 2. scalar quantity 3. vector quantity
4. centripetal force
7. centripetal acceleration 5. centrifugal force 6. angular velocity
10. gravitational field
8. center of mass 9. center of gravity

11. gravitational field intensity 12. escape velocity

2. Very short answer questions

1. Write the SI unit and CGS unit of force.
2. Write the relation between the SI unit and CGS unit of force.
3. What is a negative vector?
4. Write the SI unit and CGS unit of gravitational field intensity.
5. Give any four examples of scalar quantity.
6. Give any four examples of vector quantity.
7. What is center of gravity?
8. What is meant by stability of a body?
9. Write the SI unit of angular velocity and centripetal acceleration.
10. What is the formula used to calculate centrifugal force?
11. What is the value of the escape velocity on the earth’s surface?
12. What was the first man-made object to attain escape velocity from the earth?

20 Optional Science - 10

PHYSICS

2Step

3. Short answer questions

1. How is the magnitude of vector quantity denoted?
2. How is a vector quantity represented graphically?
3. Write the direction of centripetal force and velocity in circular motion.
4. Write four characteristics each of centripetal force and centrifugal force.
5. Write any two examples each of centripetal force and centrifugal force.
6. Write any two applications each of centripetal force and centrifugal force.
7. Write two conditions for the stability of a body.
8. Write any four real life applications of the center of gravity in the stability of a

body.

4. Differentiate between

1. Vector quantity and scalar quantity
2. Centripetal force and centrifugal force
3. Gravitational field and gravitational field intensity

5. Give reasons

1. Distance traveled is called a scalar quantity, but displacement is called a vector
quantity.

2. Mass is called a scalar quantity, but weight is called a vector quantity.
3. The graphical method for adding vectors is also called 'head-to-tail’ method.
4. Centripetal force is a real force.
5. Centrifugal force is a fictitious force.
6. A ship carries ballast in its hull.
7. The bottom of a hydrometer is made heavier.
8. A half-filled mineral water bottle is more stable than a full one or an empty one.
9. An empty vehicle can be unstable.
10. Buses are more stable than trucks.
11. Vehicles that are too tall are unstable.
12. Escape velocity is the same for all objects projected in any direction.

6. Answer the questions with the help of the given figure

1. The center of gravity of three trucks parked on a
slanted road is shown in the given figure. Which
truck will topple over?

Optional Science - 10 21

PHYSICS

2. Plot the given vectors on a graph and find their resultant using graphical method.

YL ~ A /, _ 27.5m \ B 8 - 30.0m
~
X o

3Step

7. Numerical problems

1. Find the magnitude and direction of displacement which has an x-component of 40m
and y-component of 60m.

2. A man walks 40m east and then 30m north. Find his resultant displacement.

[Ans: 50m, 37o north of east]

3. Vector →A is 3m in length and the position is along the positive x-axis. Vector →B is 4m in

length and points along the y-axis. Find the resultant vector.

[Ans: 5m, 53.13o with x-axis]

4. The mass of the moon is 7.2× 1022 kg and its radius is 1.7× 106 m. Find the gravitational

field intensity on its surface. What is the weight of a body of mass 100kg on its surface?

(G = 6.67 × 10-11 Nm2/kg2) [Ans: 1.67N/kg, 167 N]

5. The mass of the earth is 6.0 × 1024 kg and its radius is 6.4 × 106 m. Find the gravitational

field intensity at its surface. What is the weight of a body of mass 100kg on its surface?

(G = 6.67 × 10-11 Nm2/kg2) [Ans: 9.77 N/kg, 977 N]

6. The mass of the planet Jupiter is 1.9× 1027 and its radius is 7.1× 107 m. Find the gravitational

field intensity on its surface and calculate the weight of a body of mass 90kg on its

surface? [Ans: 24.14 N/kg, 2172.6 N]

7. Find the gravitational field intensity at a height of 3,600 km from the surface of the earth.
The radius of the earth is 6,400 km and its mass is 6 × 1024 kg. [Ans: 4.002 N/kg]

8. Find the gravitational field intensity at a height of 6,400 km from the surface of the earth.
The radius of the earth is 6,400 km and its mass is 6 × 1024 kg. [Ans: 2.443 N/kg]

9. What will be the gravitational field intensity of the earth if its mass could be squeezed to

the size of the moon? (Me= 6 × 1024 kg, Rm= 1.7× 106 m) [Ans: 138.4 N/kg]

8. Draw a diagram

1. to show the triangle method of vector addition.
2. to show the parallelogram method of vector addition.
3. to show the polygon method of vector addition.

4. to show the center of gravity in the following regular objects

a. circular disc b. rectangular sheet c. triangular sheet
d. rectangular bar e. cuboid

022 Optional Science - 10

PHYSICS

4Step

1. Derive the following expressions, where the terms used have their usual meaning.

a. F = mv2 b. I= GM Fc. ve = 2GM
r r2 R

2. State the triangle law of vector addition and derive expressions for the resultant

magnitude and direction.

3. State the parallelogram law of vector addition and derive expressions for the resultant
magnitude and direction.

4. Explain the mechanical way to determine the center of gravity.

5. Explain the role of the center of gravity in the stability of a vehicle.

Multiple choice questions (MCQs)

1. Who defined centripetal force? b. Isaac Newton
a. Christiaan Huygens d. Michael Faraday
c. Charles Darwin

2. The escape velocity on the earth’s surface is

a. 11,200m/s b. 11,400m/s

c. 12,100m/s d. 11,800m/s

3. The value of the universal gravitational constant is equal to

a. G = 6.67× 10-11 Nm2/kg2 b. G = 6.67× 10-12 Nm2/kg2

c. G = 6.78 × 10-11 Nm2/kg2 d. G = 6.78× 10-11 Nm2/kg2

4. The gravitational field intensity on the surface of a planet of mass 'M' and radius 'R' is

given by

a. I= GM b. I= GMm
R2 r2

c. I= GMm d. I= GMm
(r+h)2 R2

5. The value of the gravitational field intensity at the earth’s poles is

a. 9.78 N/kg b. 9.87 N/kg

c. 9.83 N/kg d. 9.38 N/kg

6. The centripetal acceleration of a body moving with an angular velocity 'ω' in a circular
path of radius 'r' is given by

a. a = rω b. a = rω2

c. a = r2ω2 d. a = r2ω

PHYSICS 0Optional Science - 10 23

7. The expression to find the centripetal force on a body of mass 'm' moving with a velocity

of 'v' in a circular path is

a. F = mv b. F = mv2
r r

c. F = mv2 d. F = mv
r² r²

8. The escape velocity on a planet of mass 'M' and radius 'R' is given by

Fa. v = GM Fb. v = GM
e R e R²

Fc. v = 2GM Fd. v = 2GM
e R e R²

9. The escape velocity depends on which of the following factors

a. mass of the object b. mass of the plane

c. angle of projection d. temperature of the planet

10. The mass of Jupiter is about 319 times that of the earth and its radius is about 11 times
that of the earth. The ratio of the escape velocity on Jupiter to that on the earth is

a. 29 b. 29

c. 1 rd. 1
29 29

Project Work

1. Take a 15 cm scale and 30 cm scale. Balance them on your figure as shown in the given
figure. Do you find the balancing point exactly at half of the length? Mark that position.
Now put that scale over a pointed support in such a way that the mark rests over the
support. Then balance that scale. Do you find the location of the center of gravity of your
scale? Mark that point and show it to your friends in the classroom.

2. Take a piece of plywood. Make a hole near the edge of the plywood and hang it on a
nail in such a way that the wood can rotate freely about the nail. Make a plumb line by
tying a weight to a piece of string. Hang the string on the nail, and mark the vertical line
with a pencil when the wood comes to rest. Make another hole at some other spot near
the plywood's edge and repeat the same procedure. The spot where the two lines cross
is the center of gravity. Put that plywood over a pointer object. Adjust the position of
the pointed object at the point of intersection of the two lines. Does your plywood get
balanced at that point?

24 Optional Science - 10

PHYSICS

UNIT

2 PRESSURE

Daniel Bernoulli (February8,1700- March 17, 1782) was a Swiss mathematician and

physicist and was one of the many prominent mathematicians in the Bernoulli family. Daniel
was sent to Basel University at the age of 13 to study philosophy and logic. He finished his
baccalaureate examinations in 1715 and went on to obtain his master's degree in 1716.

The most important work which Daniel Bernoulli did while in St Petersburg was his work
on hydrodynamics. He published the basic properties of fluid flow, pressure, density and
velocity, and gave the Bernoulli principle. One of the most common everyday applications of
Bernoulli's principle is in airflight.

Key terms and terminologies of the unit

1. Pressure: The force acting perpendicularly per unit area is called pressure, i.e.

Pressure = Force .
Area

2. Fluid: Any substance which can flow and does not possess its own shape is called

fluid.

3. Thrust: The force which acts normal to a given surface is called thrust.

4. Liquid pressure: The liquid thrust per unit area on the walls of the container is
called liquid pressure.

5. Intermolecular force: The force of attraction or repulsion between molecules is
called intermolecular force.

6. Cohesive force: The force which attracts liquid molecules to each other is called
cohesive force.

7. Adhesive force: The force which arises between liquid molecules and the
molecules of the container is called adhesive force.

8. Surface tension: It is defined as the force per unit length acting perpendicular on
an imaginary line drawn on the liquid surface, tending to pull the surface apart
along the line.

9. Viscous force: The internal frictional force exerted between liquid layers in
motion is called viscous force.

Optional Science - 10 25

PHYSICS

10. Viscosity: The property of fluids to offer resistance to objects moving through
them is called viscosity.

11. Deforming force: The external force which produces change in length, volume
and shape of a body is called deforming force.

12. Deformed body: A body which experiences a deforming force is called deformed
body.

13. Restoring force: A force developed within a body which restores the body to its
original state is called restoring force.

14. Elasticity: The property of a material to regain its original state when the
deforming force is removed is called elasticity.

15. Elastic body: The body which possess the property of elasticity is called an elastic
body.

16. Perfectly elastic body: A body which completely regains its original shape and
size after the removal of the deforming force is said to be perfectly elastic.

17. Plastic: Bodies which do not exhibit the property of elasticity are called plastic.

18. Perfectly plastic: Bodies which do not exhibit the property to return to their own
shape and size after removing the deforming force is called perfectly plastic.

19. Plasticity: The property of a body by virtue of which it tends to retain the altered
shape and size on removal of the deforming force is called plasticity.

20. Partially elastic: The bodies which partially regain their original form after
removing a deforming force are called partially elastic.

21. Elastic limit: The maximum stress that a piece of material can withstand without
being permanently deformed is called elastic limit.

22. Stress: The restoring force developed per unit area of a deformed body when
subjected to an external deforming force is known as stress.

Introduction

You had learnt already in the lower classes that the force acting perpendicularly per unit area
is called pressure. It is a scalar quantity. Its SI unit is N m-2 or pascal (Pa). Pressure is the most
important variable in our daily life. In grade 9, you learnt about pressure and some of its
consequences.

Any substance which can flow and does not possess its own shape is called fluid. The fluid
include all liquids and gases. In this chapter, we will learn about some fluid properties,
especially liquid pressure and its flow. The force of attraction between like molecules in a
liquid and that in between unlike molecules of a liquid and the container gives rise to the
surface phenomena in liquids. One of the important surface phenomena in liquids, surface
tension, is discussed in this unit.

Matter is made up of atoms or molecules. Solids have definite shape and appreciable stiffness
or rigidity. Some solids have a property to regain their shape and size after deformation within
a limit. Such a property is called elasticity. In this unit, we will learn about deforming forces,
elasticity and elastic limit, too.

026 Optional Science - 10

PHYSICS

Liquid pressure

Liquids do not maintain a fixed shape. They occupy space in a container and gain shape of
the container. When a liquid is kept in a container, it exerts a force on its walls. In liquids at
rest, force simply acts normal to the surface. The force which acts normal to a given surface is
called thrust. Liquid applies thrust on the walls of the container, which causes pressure on the
container. The liquid thrust per unit area on the walls of the container is called liquid pressure.
Liquid also exerts pressure on any object in the liquid.

Expression for liquid pressure

Let us consider a regular container having area of cross-section 'A', Volume=Ah
density of liquid be ' ρ', height of the liquid column or depth be 'h' A
and acceleration due to gravity be 'g'.

Since the thrust at the bottom of the cylinder is the same as the weight

of the liquid. Therefore, the pressure on the base of the container is

given by A

Pressure (P) = Force = Weight of liquid (W) = mg
Area Area A

= Vρg [Since mass of a liquid (m) = volume of liquid (V) × density (ρ)]
A

= Ahρg [Since volume of liquid (V) = area of cross section (A) × height (h)]
A

Pressure (P) = hρg

Thus, the pressure at a point inside a liquid is given by the product of the depth, density of
liquid and acceleration due to gravity.

Factors on which the pressure at a point in liquid depends

The pressure due to a liquid depends on three factors- depth of liquid, density of liquid and
acceleration due to gravity.

1. At a particular place, the acceleration due to gravity (g) is constant. When the acceleration
due to gravity (g) and density of the liquid (ρ) are constant, the pressure in a liquid is
directly proportional to its height. i.e., P α h (keeping 'g' and 'h' constant)

For example, the height of a water column in a tap on the upper floor is less than that
for the tap on the lower floor. So the water pressure in the upper floor tap is lower than
that in the lower floor tap.

2. When the acceleration due to gravity water cooking oil
(g) and the height of the liquid column
(h) are constant, the pressure at a point hh
in a liquid is directly proportional to its
density. i.e., P α ρ (keeping 'g' and 'h' xy
constant)
fig:variation of liquid pressure with its density

For example, one beaker is filled with water and the other is filled with oil of density 0.8
g/cm3 to the same level. If there are two identical holes at the same height on both the
beakers, the water comes out with more force due to high pressure. Hence the pressure
depends on the density of the liquid.

Optional Science - 10 27

PHYSICS

3. When the density of the liquid (ρ) and the height of the liquid column (h) are constant,
the pressure in a liquid is directly proportional to the acceleration due to gravity.

i.e. P α g (keeping 'h' and 'ρ' constant)

For example, the acceleration due to gravity varies on the basis of the distance from the
center of the earth. The acceleration due to gravity at the pole is 9.83 m/s2 and that at the
equator is 9.78 m/s2. When two identical water tanks- one at the equator and another at
the pole - are filled completely, then the pressure is more at the bottom of the tank at
the pole.
Solved Numerical- 2.1

The density of mercury is 13,546 kg/m3. Find the pressure exerted by the mercury column of
height 760 mm. What height of the water column will exert the same pressure?
Solution:

Here, density of water (ρ) = 13,546 kg/m3

Height of the mercury column (h) = 760 mm = 760 = 0.76 m
1000
The liquid pressure is given by

P = hρg

Or, P = 0.76 × 13,546 × 9.8

∴ P = 100890.6 Pa

Pressure of the mercury column (P) = 100890.6 Pa

Height of the water column to exert the same pressure of 100890.6 Pa is given by

100890.6 = h × 1000 × 9.8
h = 1090880900.6= 10.3 m
Therefore, the height of the water column to exert the pressure of 100890.6 Pa is 10.3 m.

Properties of liquid pressure

Liquid pressure does not depend on the shape of the container. It acts in all directions
and remains the same for all directions. Liquid pressure applies force at 90o to any
contact surface.

Some consequences of liquid pressure

i. Deep sea divers wear a stout steel suit

The liquid pressure is directly proportional to the depth from its free surface. The
deeper an object is in water, the greater the pressure acting on the object. This effect
is experienced by the deep seadivers. They feel the increasing water pressure on their
body while swimming deeper under water. This may cause some blood vessels to burst,
resulting in bleeding. Thus, they wear a special kind of suit to counter the high pressure
at great depths in the sea.

ii. Walls of a dam are made thicker at the bottom dam wall is
made thicker
Water pressure increases with depth. When water is stored in a dam, at the bottom

then there is high pressure at its bottom. It exerts more force on the

dam. Therefore, to withstand the high pressure exerted by the water

at greater depth, the walls of a dam is made thicker at the bottom.

028 Optional Science - 10

PHYSICS

iii. Water supply tank is placed at a height

In a city area, water supply tanks are placed at a higher point as compared to the heights
of the buildings in the area. Water pipes are distributed in different regions of the area
to supply water. When tanks are placed at a greater height, the pressure of water will be
large enough to force the water to rise up the multi-storeyed buildings.

In case of the water tanks in tall buildings, water tanks are placed at the top. This
increases the height of the water column in the water pipes of the building. Due to
this, water pressure on the taps increases, and it helps to fill water faster and to take a
shower.

Types of molecular force

Every matter is made up of minute particles called molecules. These molecules exert a force on

one another. The force of attraction or repulsion between the molecules is called intermolecular

force. Such a force is in between like molecules as Adhesion
well as unlike molecules. On the basis of the type of Cohesion
interacting molecules, the intermolecular forces are

classified into: cohesive force and adhesive force. -.-.-..:.:.-i..:....._....i.i._.w...._ Adhesion

Cohesive force fig:adhesion and cohesion

The force which attracts liquid molecules to each other c5- ·o· .. 5 -
is called cohesive force. It is also known as a force of
cohesion. Cohesive force makes liquid molecules cling ti" 8+- / ',._, 8+-
together. It is responsible for the formation of liquid ,._,
drops and surface tension. 0"'+H/ ' H0"'+

··•.. c5- ......
~intramolecular ··..•Q......- ~

The attractive force varies in magnitude, depending on polar covalent ' --...._/ , hydro9en
H bondin9
the substances concerned. Solids have a strong force of bondin9 H

c5+ c5+

cohesion. That's why they have a definite shape and fig:Intermolecular forces in water

size. In the case of liquids, cohesive force among the molecules is relatively weaker. This makes

possible for the free movement of molecules within the volume of liquids. During such free

movement, molecules do not go out of the liquid surface. That's why liquids have a definite

volume but no definite shape. The cohesive forces are least amongst the molecules of a gas.

Adhesive force

The force which arises between liquid molecules and the molecules of the container is called
adhesive force. It is also known as the force of adhesion. Adhesive forces make the liquid wet
the surface of its container. Adhesive force is responsible for capillary rise. For example, water
wets a glass surface. This is due to the adhesive force between the water molecules and the
glass molecules. The adhesive force is more than the cohesive force in this case. By waxing the
glass surface, we can reduce the adhesive force and allow the cohesive force between the water
molecules to pull the surface into spherical drops.

Adhesive force is different for different substances. For example, the adhesive force between
the gum and a solid surface is stronger than that between water molecules and a solid surface.
That’s why gum is used to paste paper, photographs, etc.

Optional Science - 10 29

PHYSICS

The surface phenomenon of liquids: Surface tension

We observe that liquids form drops, water wets some surfaces but run off others, pond-skater
or water strider insects rest on the surface of water without sinking, water rise up a capillary
tube but mercury is pushed down to a lower level in a capillary tube. This is due to the tension
on the surface of a liquid. The surface of a liquid behaves as though it is covered by a stretched
membrane.

Molecular theory of surface tension: Cause of existence of tension on the surface of a liquid

The exposed surface of a liquid in a container acts like a stretched membrane B
that exerts force on the liquid enclosed. This is due to the force of attraction
between the surface molecules and neighboring molecules of the fluid.

In the given figure, the wholly submerged molecules have attractive forces

in all direction. Such forces are canceled out. Therefore, the net force on A

the wholly submerged molecules is zero. On the free surface, the number

of molecules in the lower half of the sphere is more and the upper half is

completely outside the surface of the liquid. Therefore, all the molecules lying on the surface

of a liquid experience only a net downward force. So horizontally, they attract each other

and act like a membrane. The free surface of a liquid tends to assume minimum surface area

by contracting and remains in a state of tension like a stretched elastic membrane. Thus, the

surface tension is mainly caused by the unbalanced cohesive force acting near the top surface

of the liquid.

Surface tension

The surface of a liquid behaves like a stretched rubber sheet. The TI I T
tension of the surface of a liquid can be measured by the concept
of tension of a stretched rubber sheet. The tension on a rubber
sheet is always measured in terms of the pull that is exerted on
a certain length of the boundary. The larger the length under
consideration, the greater is the pull.

Surface tension is the property of the free surface of a liquid at rest to behave like a stretched

membrane in order to acquire minimum surface area. It is due to the attractive force exerted

upon the surface molecules of a liquid by the molecules beneath that. Such a force tends to

draw the surface molecules into the bulk of the liquid. Imagine a line AB on the free surface

of a liquid at rest as shown in the given figure. Surface tension is measured as the force acting

per unit length on either side of this imaginary line AB. The force is perpendicular to the line

and tangential to the liquid surface. If F is the force acting on the length l of the line AB, then

surface tension is given by

T= F
l
Thus, surface tension is defined as the force per unit length acting perpendicular on an

imaginary line drawn on the liquid surface, tending to pull the surface apart along the line.

Memory Plus

The SI unit of surface tension is newton per meter, denoted by N/m and the CGS unit is
dyne/cm.

030 Optional Science - 10

PHYSICS

Experiments to demonstrate surface tension

Liquid surface behaves like a stretched elastic skin and tends to have a minimum surface area.
It can be demonstrated by the following simple experiments and observations:

1. Floating a needle or a paper clip

Have you ever dropped a sewing needle or a paper clip horizontally in water? If you
have, did it sink? Obviously, an iron needle sinks when you drop it into water. Now try
it with full caution. Is it possible to make a needle or paper clip float?

Materials required: a glass tumbler, water and a sewing needle or paper clip

Procedure:

1. Fill a trough half with water.

2. Rest the steel needle on a small piece of blotting or filter paper and gently place it
on the surface of water.

After a while, the soaked paper sinks, leaving the needle floating
on the surface. Look carefully at the water surface around the
floating needle, do you observe the surface depressed? The
surface of water is depressed and stretched like an elastic skin.
The stretched elastic surface provides a stronger upward force
to support the needle. It is different from the upthrust from
the displaced water. What do you observe after adding some
drops of dish soap into water?

Explanation: The magnitude of pressure exerted by an object depends on its weight and
contact area. A steel needle has a small contact area when we drop it vertically, which
leads to a large pressure on the surface of water. It tears the stretched surface of the
water and the needle sinks to the bottom of the water. On the other hand, if it is kept
horizontally on the water surface with full caution, the contact area increases and
pressure exerted on the water surface becomes less. In this case, the stretched water
surface is not torn. As a result the needle floats in water.

When some drops of dish soap are added in Volume of water displaced
the water, the cohesive force between the water membrane
molecules decreases, and the surface tension also
decreases. So the needle or paper clip will sink in fig:floating needle on surface of water
the water.

2. Clinging of hairs of a painting brush
Materials required: Water, beaker and a painting brush

Procedure

1. Dip a painting brush into water. Do you observe that its
hairs get separated from each other?

2. Take the brush out from the water and observe the hairs

again. Do you observe them clinging together this time? fig:Clinging of hairs of a
painting brush

Optional Science - 10 31

PHYSICS

Explanation: When a painting brush is dipped in water, its hairs get separated from
each other. When the brush is taken out of water, it is observed that its hairs will cling
together. This is because the free surface of the water film tries to contract due to surface
tension.

3. Water drops on a coin

Have your ever tried to fit water drops on a coin? How many drops can you fit on a
coin? Do it practically.

Materials required: Coin, water in a beaker and a medicine dropper

Procedure:

1. Add one drop of water on a coin. Does it fit on your coin?

2. Continue adding drop scarefully until the water spills off the coin.

3. Repeat it 2 more times. Finally find the average number of drops that can fit on a
coin.

Explanation: Water molecules pull each other due to cohesion. At the same time, the
molecules on the surface form a stretched layer, which produces surface tension.

Consequences of surface tension

1. The drips from a tap are round droplets: A drop or droplet is a small
column of liquid, bounded completely, or almost completely, by free
surfaces. Surface tension pulls the drips from a tap into round
droplets.

2. Meniscus effects: Meniscus effects are due to surface tension. Any -Concave Convex
meniscus
water surface in contact with a vertical glass wall curves up to meet meniscus Mercury
the wall. Mercury in contact with a vertical glass wall curves down
to meet the glass. But the remaining surface remains stretched like a

membrane. This gives rise to a concave or convex meniscus.

3. Tendency of liquid to assume spherical shape: In the case of liquid outside a container,
it is spherical in shape like a rain drop. For example, small drops of mercury are
spherical. A drop of mercury is governed by two factors- surface tension and gravity.
Gravity pulls the molecules downward, and it tries to spread the liquid, while the
surface tension tries to collect it in the form of a sphere so that it has minimum surface
area. When we touch a mercury drop with a needle, a dimple is formed at the point of
contact, which disappears as soon as we remove the needle. Such a drop behaves like
an inflated rubber balloon.

4. Formation of lead shots: A shot is a collective term for small balls, or pellets, often
made of lead. A lead shot is also used for a variety of other purposes, such as filling
cavities with dense material for balance. For example, a bulb of a hydrometer is filled
with lead shots to keep it upright in water. The lead shot was
originally made by pouring molten lead through screens into water
from a sufficient height. During its fall, the molten lead forms small
spherical drops due to surface tension forces, and on entering water,
they become solid.

32 Optional Science - 10

PHYSICS

5. Surface tension minimizes surface to form bubbles: Bubbles are held together by
surface tension. A small soap bubble in air forms a sphere. Surface tension in the film
acts to reduce the bubble size. So its internal pressure must be greater than the pressure
outside.

6. Water striders or pond skaters are able to walk on water:
They rest on the surface of water without breaking it. A
dimple is formed where the surface is stretched by the
insect's feet. The surface tension causes the insect's feet to
make indentations on the water surface and has the same
characteristic as that of an elastic balloon surface.

7. Separation of oil and water: Surface tension of oil is less than that of water. The
separation of oil and water is caused by the difference in surface tension of the two
liquids. When a drop of oil is dropped on the surface of water, due to higher surface
tension of water, the oil is stretched in all directions as a thin film. Thus oil makes a thin
film when it spreads in water.

8. Mosquitoes breed on the free surface of stagnant water: .........•' ,-•"-'.-,-.,,~..._....../
Due to surface tension, the surface of water acts like a
stretched layer. It can support the eggs laid by mosquitoes. ,/
On spreading oil in water, it makes a thin layer on the surface
of water. Such a film of oil is of low surface tension. So
mosquitoes cannot breed on the oiled surface of water.

9. Lubricating oils spread easily: Lubricating oils spread easily to all parts because of
their low surface tension.

10. Antiseptics spread easily: Liquids with low surface tension spread easily. So the
surface tension of antiseptics like Dettol is kept low so that it can be easily spread on

the wounds.

Factors affecting surface tension

1. Temperature: Surface tension decreases with rise in temperature. For example, the
surface tension of hot soup is less than that of cold one. It spreads over a larger area of
the tongue of a person. That makes hot soup more tasty than the cold one.

2. Contamination: Contamination like oil on water, mixing of grease and dust, etc. reduce
the surface tension of water. This reduces the force between the water molecules. For
example, a floating paper clip on water sinks by adding some amount of detergent in it.
But the surface tension of water increases slightly on adding salts like common salt in it.

Viscosity

Activity

1. Take a beaker filled with 2/3 rd of water and put a glass rod in it. Stir it to set the water in
rotation. Do you see that water rotating in the form of co-axial cylindrical layers?

2. Stop stirring. Do you observe that the speed of the innermost cylindrical layer is
maximum?

The speed of successive layers of water decreases gradually as we observe from the center
of the beaker to its wall. After sometime, the water comes to rest. This is due to the internal
friction between the liquid layers.

Optional Science - 10 33

PHYSICS

Have you ever noticed the flow of water and that of gum? Water flows more easily than gum.
Some liquids flow more easily than others. Such flow of liquid involves different parts flowing
with different velocities. These parts slide past each other, as if they were in layers. If there is
little friction, the layers slide past each other with ease. But it is difficult in the case of more
friction between the two layers. Fluids in which the flow is difficult are called more viscous
fluids. For example, gum, syrup, etc. On the other hand, fluids in which the flow takes place
with ease are said to be less viscous fluid. For example, water, petrol, etc. More viscous fluids
offer more resistance to an object moving through them. The property of fluids to offer
resistance to objects moving through them is called viscosity.

Memory Plus

The internal frictional force exerted between the liquid layers in motion is called viscous force.

Viscosity is the property of a liquid in motion. Inside a fluid, viscosity is the property of a fluid
by virtue of which it opposes the relative motion between its adjacent layers. It acts on the
fluid between the slower and faster moving adjacent layers.

Cause of viscosity

There is intermolecular force of attraction between the liquid molecules. The different layers
of a liquid move with different velocities. The layer of liquid in contact with the wall is at rest,
while others above it move with increasing velocity. Due to intermolecular force of attraction,
every fast moving layer tries to move the next layer with it faster. Whereas every slow moving
layer tends to retard the adjoining fast moving layer of the liquid. Thus the internal tangential
force between the two adjacent layers of a liquid, called viscous force, is the cause of viscosity.
Examples of viscosity

1. A stirred liquid, when left, comes to rest due to viscosity.

2. Viscosity of air is less than that of water. So we can run fast in air but not in water.

3. Liquids differ in viscosity. Some liquids (e.g. water) flow more easily than others (e.g.
honey).

4. Honey and oil flow more easily at higher temperatures as increase in temperature
decreases viscosity.

Applications of viscosity

1. Viscosity of blood can be used to detect blood corpuscle deficiency.
2. An oil with suitable value of viscosity is used as a lubricant in engines.

3. The viscosity of oil helps in applying brakes.
Measurement of viscosity of a liquid

Viscosity is a measure of how viscous a fluid is. It measures the resistance of a fluid to a body,
which moves through it. It is easier to move an object through a thin fluid with a low viscosity
(e.g. water) than through a thick fluid of high viscosity (e.g. honey).

Viscosity is measured in terms of pressure and time. Under a given pressure, a more viscous
liquid will take more time to move a given distance than a less viscous one. It can also be
measured in terms of time taken for an object with a given size and density to fall through the
liquid of interest.

34 Optional Science - 10

PHYSICS

Memory Plus

A viscometer is an instrument used to measure the viscosity of a fluid. It is also called
viscosimeter. The SI unit of measurement of viscosity is Ns m-2. It is also called pascal
second (Pa s) or decapoise. In the CGS system, its unit is dynes-s cm-2, also called a poise.

1 decapoise = 10 poise

Factors affecting viscosity

Viscosity is affected by the size and shape of the molecules, the interactions between them and
temperature.
1. Shape and size of molecules: Fluids with larger, more complex molecules have

higher viscosities. For example, long, chain-like molecules in polymers and the
heavier hydrocarbon compounds have high viscosity.

2. Interaction between molecules: A fluid with strong intermolecular force does not
flow easily. Such a fluid has high viscosity. It is the chemical bond that determines
the viscosity of a particular fluid. Polar compounds can form hydrogen bonds that
link separate molecules together. This increases the overall resistance to the flow and
movement. For example, long molecules with noticeable polarity, such as glycerin and
propylene glycol have high viscosity.

3. Temperature: Temperature has a major effect on viscosity. Viscosity of a substance is
expressed at a fixed temperature. In liquids, it decreases with temperature. For example,
syrup or honey moves easily when they are heated.

Know the Reason

Viscosity of liquids decreases with increase in temperature, why?
On increasing the temperature of a liquid, the molecules move apart, and the intermolecular
force decreases. They spend less time in contact with one another. So viscosity of liquids
decreases with increase in temperature.

Viscosity of gases increases with increase in temperature, why?
At high temperature, the gas molecules move faster, and there are more collisions between
them. Resistance to movement in gases increases with increase in temperature, which
reduces their ability to flow. So viscosity of gases increases with increase in temperature.
Water has low viscosity, why?
Water is a polar molecule, but it has low viscosity because of the small molecules.

Elasticity

Different types of external forces act on a number of bodies in our surrounding. Such external
forces may produce change in the length, volume and shape of the body. The external force
which produces change in the length, volume, and shape of a body is called deforming force.
When a deforming force is applied on a body, which is not free to move, the shape or size of
the body changes. A body which experiences a deforming force is called deformed body.

Optional Science - 10 35

PHYSICS

A relative displacement of particles takes place when an external force is applied on a body,
which is not free to move. If the particles are displaced with a certain limit, they regain their
original position after the deforming force is removed. When the deforming force is removed,
the body regains its original state due to the force developed within the body. Such a force
developed within a body, which restores the body to its original state, is called restoring force.
The property of a material to regain its original state when the deforming force is removed is
called elasticity. The body which possess the property of elasticity is called an elastic body.

Cause of elasticity

Matter is made up of atoms or molecules. The space between atoms or molecules varies in
different types of matter. Hence, the force of attraction between the molecules also varies. The
average location of the molecules in a solid material does not change with time. They are
packed together, their kinetic energy is also very small. This gives a definite shape and
appreciable stiffness or rigidity. Due to this rigidity, matter tends to regain the shape and size
when an external force tries to change its configuration.

Spring-ball system concept of elasticity: When the deforming

forces on the atoms in a solid are removed, the interatomic forces

bring them back to their original position. Such a mechanism can

be visualized by taking a model of the spring-ball system as shown

in the given figure. In the figure, the balls represent the atoms and

the springs represent interatomic forces. If we try to displace any

ball in the system from its equilibrium position, the spring system

tries to restore the ball back to its original position. fig:spring ball concept of elasticity

Some examples of elasticity

1. When we stretch a rubber band, its length increases. On removing the deforming force,
it comes back to its original length.

2. When a rubber ball is pressed, it gets deformed. But it regains its shape on removing
the deforming force.

3. An archer bends the bow to shoot an arrow. The bow springs return back to their
original form when the arrow is released.

4. When a steel wire is loaded at one end by keeping the other end fixed, then it gets
deformed. But it regains its original length on removing the changed load. Steel is
highly elastic. So springs are made of steel.

In the above examples, the rubber band, rubber ball, bow and steel are elastic objects.

Perfectly elastic body

The extent to which the original form of a body is restored, when the deforming forces are
removed, is not the same for all materials. It varies from material to material. A body which
completely regains its original shape and size after the removal of the deforming force is said
to be perfectly elastic. There are no perfectly elastic bodies. It is an ideal concept only. Quartz
fiber and phosphor bronze (an alloy of copper with tin and phosphorus) are nearly perfectly
elastic bodies. Phosphor bronze is used for suspension purpose. In very sensitive instruments,
quartz fiber is used in place of phosphor bronze.

036 Optional Science - 10

PHYSICS

Perfectly plastic body

Do you have any experience in clay art? We can give shape to clay while making a design. Wet
clay does not show any tendency to regain its original configuration after deformation. Bodies
which do not exhibit the property of elasticity are called plastic. For example, perfectly wet
clay is highly plastic. Bodies which do not exhibit the property to return to their own shape
and size after removing a deforming force are called perfectly plastic. Putty, semi-solid coal
tar, paraffin wax are examples of nearly plastic bodies. Such bodies retain their deformed
shape and size. The property of a body by virtue of which it tends to retain the altered shape
and size on removal of a deforming force is called plasticity.

Memory Plus

Bodies which partially regain their original form after removing a deforming force
are called partially elastic. Actual bodies have elasticity in between the limit of perfect
elasticity and perfect plasticity.

Material Parameters that Determine Elasticity

Most materials which possess elasticity in practice remain purely elastic only up to very small
deformations. In engineering, the amount of elasticity of a material is determined by two
types of material parameter.

1. Modulus of elasticity: It measures the amount of force per unit area needed to achieve
a given amount of deformation. It is used to describe the elastic properties of objects
like wires, rods or columns when they are stretched or compressed. The SI unit of a
modulus is pascal (Pa). The higher the modulus of elasticity of the material, the greater
the rigidity. Such material is harder to deform. It means more force must be applied to
produce a given deformation. For example, the modulus of elasticity of steel is about
200 GPa(depending on the kind of steel). So it is suitable for the most bridges with the
longest spans.

2. Elastic limit: If an elastic material is stretched or compressed beyond a certain limit, it
will not regain its original state and will remain deformed. The maximum stress that a
piece of material can withstand without being permanently deformed is called elastic
limit. SI unit of elastic limit is pascal (Pa).

Stress

Relative displacement of the particles in a body takes place when an external force acts on
it. The body is, thus, said to be deformed. In a deformed body, a restoring force is set up
within the body, which tends to bring the body back to the normal position. This is due to the
property of elasticity. The magnitude of these restoring forces depends upon the deformation
caused. The restoring force is equal in magnitude, but opposite in direction to the external
forces. This restoring force developed per unit area of a deformed body when subjected to an
external deforming force is known as stress.

In a position of equilibrium, the restoring force is equal to the external impressed deforming
force. Thus, stress is measured by the magnitude of the deforming force acting on a unit area
of the body. i.e.,

PHYSICS 0Optional Science - 10 37

Stress = Restoring force = F
Area A

Where 'F' is the deforming force acting on an area 'A' of the body.

Memory Plus

In SI, the unit if stress is Nm-2 and in the CGS system its unit is dyne cm-2.

Hooke's law

The law of elasticity was discovered by the English scientist Robert Hooke in 1660. It states

that, within elestic limit, the displacement or size of the deformation is directly proportional

to the deforming force or load.

Mathematically, Hooke’s law states that the applied force 'F' F= kx

equals a constant 'k' times the displacement or change in length

'x', i.e F = kx. 'k' is called the spring constant. Its value depends not

only on the kind of elastic material under consideration but also 0

on its dimensions and shape. Hooke’s law can also be expressed x
as F = −kx. Where 'F' is the restoring force of spring. The negative F 2x

sign indicates that the force acts in opposite direction of the •2F

displacement. fig:demonstration of Hooke's law
Force-extension graph to determine elastic limit

A spring supported by a rigid support is loaded with varying loads. As the load increases, the
extension of the spring also increases. The relation between tensile stress and extension of a
wire can be shown in the form of a graph as shown in the given figure. Looking at the graph,
we can determine the elastic limit of the spring.

1. Below the elastic limit: In this region, 10
the extension is proportional to the 8
force. If the load is removed, then
the spring will go back to its original E
length. Within this region, the graph is
a straight line (OE) passing through the
origin.

2. Beyond the elastic limit: Beyond the Weight (N)
elastic limit, a spring shows plastic
behavior. When the load or applied O 0 .5 1.0 1.5 2.0 2 .5
force exceeds the elastic limit, then the
spring stays deformed. It does not go Extension(cm)
to its original length on removing the
hanged loads. Beyond the elastic limit, fig:force-extension graph
the line curves off.

38 Optional Science - 10

PHYSICS

Answer writing skill I

1. On what factors does liquid pressure depend?

Liquid pressure is given by
P = depth(h) × density of liquids (ρ) × acceleration due to gravity (g)
So liquid pressure depends on,
i. depth of liquid,
ii. density of liquids, and
iii. acceleration due to gravity

2. What is an elastic material?

An elastic material is one which when bent or stretched slightly goes back to its original
shape. For example, a rubber band, spring, etc.

3. Which force is responsible for the elastic behavior of substances?

Restoring force is responsible for the elastic behavior of substances. It is the force which
tends to restore the original configuration of the body.

4. Define plasticity.
The property of the material body by virtue of which it does not regain its original
configuration when the external force acting on it is removed is called plasticity

5. Write differences between cohesive force and adhesive force.

Cohesive Force Adhesive Force

The force which attracts liquid molecules The force which arises between liquid

to each other is called cohesive force. molecules and the molecules of the

container is called adhesive force.

Cohesive force makes liquid molecules Adhesive forces make a liquid wet the

cling together. surface of its container.

It is responsible for the formation of liquid Adhesive force is responsible for capillary

drops and surface tension. rise.

6. At a particular depth of a river and sea, water pressure is more in the case of the sea.

When the acceleration due to gravity (g) and the height of the liquid column (h) are
constant, the pressure at a point in a liquid is directly proportional to its density, i.e.,
Pαρ. Sea water has deposits of salt, and its density is more than that of river water. So,
at a particular depth of a river and sea, water pressure is more in the case of the sea.

7. A water tank is kept on the roof of a five-storeyed building and the taps on the walls
are fixed at the same height on each of the floors. The water pressure on the tap of the
ground floor is 80,000 Pa whereas the water pressure on the tap of the third floor is
11,400 Pa. Find the height of the third floor. [ Ans: 7 m]

PHYSICS 0Optional Science - 10 39

Solution:
Here, pressure on the tap of the third floor (P1) = 11,400 Pa
Pressure on the tap of the ground floor (P2) = 80,000 Pa
Let, the depth of water column up to the tap on the third floor = h1
The depth of the water column up to the tap on the ground floor = h2
Now the difference in pressure is

P2 – P1 = h2ρg – h1ρg = (h2 – h1)ρg

Or, 80000 – 11400 = (h2 – h1) × 1000 × 9.8

Or h2 – h1 = 68600 = 7m
9800

Therefore, the height of the third floor is 7m.

8. How does the knowledge of the factors affecting liquid pressure help us in our
practical life? Explain your view in two points.

In city areas, water supply tanks are placed at a higher point as compared to the heights
of the buildings in the area. When tanks are placed at a greater height, the pressure of
water will be large enough to force the water to rise up the multi-storeyed buildings.

Water pressure increases with depth. When water is stored in a dam, then there is high
pressure at the bottom. It exerts more force on the dam. Therefore, to withstand the high
pressure exerted by the water at greater depth, the wall of a dam is made thicker at the
bottom.

040 Optional Science - 10

PHYSICS

_Exe_rcis_e J_Q_ - - - - - -

1Step

Define 2. Pressure 3. Liquid pressure
1. Fluid 5. Surface tension 6. Deforming force
4. Intermolecular force 8. Restoring force 9. Elasticity
7. Deformed body 11. Viscosity 12. Viscous force
10. Plasticity
13. Stress

Very short answer questions

1. Write the SI unit of the following:

a. Pressure b. Surface tension

c. Viscosity
2. Write the formula to calculate

a. surface tension b. stress

3. On what factors does liquid pressure depend?

4. Give two examples of surface tension.

5. What is an elastic body?

6. Give two examples of elasticity.

7. What is meant by plastic body?

8. Give two examples each of a more viscous fluid and less viscous fluid.

9. Write two examples of elasticity.

10. Out of two fluids; water and honey, which one has more viscosity?

11. Name a device which is used to measure the viscosity of fluid?

12. State Hooke’s law?

13. Write two examples each of bodies which are almost perfectly elastic and perfectly
plastic.

Optional Science - 10 41

PHYSICS

2Step

Short answer questions

1. How do each of following factors affect liquid pressure? Write with an example.

a. The density of a liquid

b. The height of a liquid column

c. The value of acceleration due to gravity

2. Give two examples of each in which cohesive force is dominant and adhesive force is
dominant.

3. Mention any four consequences of surface tension.

4. How is surface tension applicable? Give two supporting examples.

5. Write in short about the two factors which affect each of following

a. surface tension. b. viscosity c. elasticity

6. Write the conclusion that can be obtained from the force-extension graph.

Differentiate between

1. Cohesive force and adhesive force
3. Elasticity and plasticity
4. Perfectly elastic and perfectly plastic

Give reason
1. Shape of a water droplet is formed on a waxed surface.
2. When a painting brush is dipped in water, its hair gets separated from each other, but

when it is taken out of water its hairs cling together.
3. Mosquitoes can breed on the surface of water.
4. Antiseptics have low surface tension.
5. Viscosity of liquids decreases with increase in temperature.
6. Viscosity of gases increases with increase in temperature.

3Step

Numerical problems

1. Find the pressure due to mercury column of height 76 cm in a mercury barometer.
(Density of mercury = 13.6 gm/cm3 and acceleration due to gravity = 9.8 m/s2)

[ Ans:101292.8 Pa]

2. Calculate the pressure exerted by a mercury column of height 750 mm at its bottom.

042Given that the density of mercury is 13.6 g/cm3 and g = 9.8 m/s2. [Ans: 9.99 x 104 Pa]

Optional Science - 10

PHYSICS

3. If the pressure exerted by the water at the bottom of Taudaha Lake is 9.8 × 104 pa, calculate

the depth of this lake. [Ans: 10 m]

4. A water tank is kept on the roof of a five-storeyed building and the taps on the walls

are fixed at the same height on each of the floors. The water pressure on the tap of the

ground floor is 1,15,600 Pa whereas the water pressure on the tap of the fourth floor is

7,800 Pa. Find the height of the fourth floor. [ Ans: 11 m]

Draw a diagram
1. To show meniscus of water in a test tube.
2. to show meniscus of mercury in a test tube.

4Step

1. Derive the formula to calculate liquid pressure. The symbols used in the formula have
their usual meaning.

2. Explain an experiment to show the effect of depth in liquid pressure.
3. What is Molecular Theory of Surface Tension? Explain it in detail.
4. How can you demonstrate the effect of surface tension?
5. What is the cause of viscosity? Explain in short.
6. What is the cause of elasticity? Explain in short.
7. Explain the relation between the force applied on a spring and extension

Multiple choice questions (MCQs)

1. The force of cohesion is b. maximum in liquids
a. maximum in solids d. maximum in gases

c. same in different matters

2. The phenomenon due to which exposed surface of a liquid, contained in a vessel, behaves

like a stretched membrane is called

a. viscosity b. surface tension

c. elasticity d. plasticity

3. Water wets the surface of glass, due to the force of :

a. adhesion b. gravitation

c. cohesion d. none of the above

4. The molecules of ink stick to the molecules of paper, due to the force of:

a. adhesion b. gravitation

c. cohesion d. none of the above

5. In the given figure, there are four containers filled with different liquids. Look at the

surface shape, in the case of which liquid is the cohesive force maximum?

a. 1 b. 2

PHYSICS 0Optional Science - 10 43

c. 3 d. 4

6. Insects are able to stand and walk on the water surface due to

a. adhesion b. gravitation

c. cohesion d. surface tension

7. Cause of viscosity in fluids is b. adhesive force
a. cohesive force

c. gravitational force d. diffusion

Project Work

Surface tension of water and alcohol
1. Take 2 coins, 2 medicine dropper, water, alcohol and a piece of paper.
2. Place the two coins on the piece of paper. Use the dropper to drop alcohol and water on

the two coins individually.
3. Count the number of water drops and alcohol drops until they just begin to overflow.

Which liquid can adjust more drops on the coin’s surface? Write your conclusion and
explain about the surface tension of water and alcohol in your classroom.

Floating razor blade on water
1. Take water, beaker and a razor blade
2. Fill a beaker half with water.
3. Put a razor blade slowly in the position shown in the given figure. Does the razor blade

float on water?

44 Optional Science - 10

PHYSICS

UNIT

3 ENERGY

Mark Zachary Jacobson, born in 1965, is a professor of civil and environmental engineering
at Stanford University and director of its Atmosphere/Energy Program. He develops
computer models to study the effects of different energy technologies and their emissions
on air pollution, weather, and climate. In a paper published in the journal, Nature, in 2001,
Jacobson theorized that black carbon, which is emitted during fossil fuel, biofuel and
biomass burning, may be the second leading cause of global warming after carbon dioxide.
Jacobson has also developed roadmaps to transition the world as a whole, all 50 U.S. states,
and 139 countries to 100% clean, renewable wind, water and solar (WWS) energy for all
energy purposes. His proposed transition will also eliminate millions of premature deaths
worldwide each year caused by air pollution and reduce disruption associated with fossil
fuel shortages.

Key terms and terminologies of the unit

1. Energy: Energy is the ability to do work.

2. Non-renewable sources of energy: The energy sources which occur in limited
and exhaustible amounts are called non-renewable energy sources.

3. Fossil fuels: Sources of energy like coal, petroleum and natural gas, which are
formed from the remains of living beings buried inside the earth’s crust for
millions of years, are called fossil fuels.

4. Fossil fuel energy: Energy from burning coal, petroleum or natural gas is called
fossil fuel energy.

5. Nuclear energy: The energy stored in the nucleus of an atom is called nuclear
energy.

6. Renewable sources of energy: Sources of energy, which are being produced
continuously in nature and are inexhaustible are called renewable energy
sources.

7. Alternative energy sources: Sources of energy which are available in nature
and can be used instead of non-renewable energy sources are called alternative
energy sources.

Optional Science - 10 45

PHYSICS

8. Hydroelectricity: The electrical energy generated by rotating turbines connected
to the generators with the help of moving water is called hydroelectricity.

9. Biofuel: Fuels like wood, biogas, alcohol, etc. from biomass of plants and animals
are called biofuels.

10. Biomass: Biomass is any organic matter that can be obtained from living organisms.

11. Biomass energy: Energy released from biomass by combustion or other chemical
processes is called biomass energy.

12. Biogas: Biogas is a mixture of gases like methane (CH4), carbon dioxide (CO2),
hydrogen (H2) and hydrogen sulphide (H2S).

13. Biogas plant: A biogas plant is a combination of a digester and gas holder, where
biogas is produced from animal dung, human excreta, industrial and domestic
wastes.

14. Briquette: A briquette is a compressed block of coal dust, or other combustible
biomass materials, such as charcoal, sawdust, wood chips, peat, or paper, used
for fuel.

15. Charcoal briquette: A charcoal briquette is a compressed block of charcoal.

16. Biomass briquette: A block of flammable matter prepared by densification of
woody biomass, leafy biomass and agricultural residues is known as biomass
briquette.

17. Briquetting plant: A briquetting plant is the technology to convert all types of
agro forestry waste into solid fuel.

18. Solar energy: Solar energy is the light and heat received by the earth from the sun.

19. Solar devices: Those devices which convert solar energy into other forms of
energy are called solar devices.

20. Wind energy: Energy received from the movement of the wind across the earth is
called wind energy.

Introduction

Energy is important in everyone's life to carry out different works. Living beings need energy
for their survival and growth. Non-living things like motorcycles, tractors, buses, trucks,
aeroplanes, etc. require fuel for their running. Energy is the ability to do work.

Living beings obtain energy from their food. Non-living things, like a vehicle, run on fuel.
There are different forms of energy, like fossil fuel energy, solar energy, nuclear energy,
wind energy, electrical energy, which are important to us. Such forms of energy are obtained
from a number of sources. In this unit, we will learn about types of energy sources, different
alternative sources of energy, their uses, advantages and disadvantages.

046 Optional Science - 10

PHYSICS

Classification of energy sources

Some of the energy sources cannot be generated in a short period of time. Whereas the others
can be replenished in a short period of time. So there are mainly two types of energy sources.
They are non-renewable energy sources and renewable energy sources.

Non-renewable energy sources

The energy sources which occur in limited and exhaustible amounts are called non-renewable
energy sources. Such energy sources cannot be generated in a short period of time. They cannot
be used again and again. Fossil fuel, nuclear fuel, etc. are the examples of non-renewable
sources of energy.

Sources of energy like coal, petroleum and natural gas, which are formed from the remains of
living beings buried inside the earth’s crust for millions of years, are called fossil fuels. They
are formed by natural processes such as anaerobic decomposition of buried dead organisms.
Fossil fuels contain high percentages of carbon. Other commonly used derivatives of fossil
fuel include kerosene and propane.

Renewable sources of energy

The sources of energy, which are being produced continuously in nature and are inexhaustible,
are called renewable energy sources. For example, wood, charcoal, many agricultural wastes.
Such energy sources can be replenished in a short period of time.

Alternative energy sources

The present rate of fossil fuel consumption is high. This will invite an energy crisis in the near
future. To avoid this, we need to find sources of energy which can replace fossil fuel. The
sources of energy which are available in nature and can be used instead of non-renewable
energy sources are called alternative energy sources. Renewable sources of energy are
also called alternative sources of energy. The government of Nepal has made its policy to
promote alternative sources of energy for conservation of energy sources. Alternative Energy
Promotion Centre (AEPC) is a Government institution established on November 3, 1996 under
the Ministry of Science and Technology with the objective of developing and promoting
renewable/alternative energy technologies in Nepal.

Hydroelectricity

Water collected in a dam at a certain height possesses potential energy. When it is allowed
to fall through a tunnel, then it has kinetic energy. This energy can be used to rotate turbines
connected to a generator. The electrical energy generated by rotating turbines connected to
the generators with the help of moving water is called hydroelectricity. A hydroelectricity
generating station, which utilizes the potential energy of water at a high level, is known as a
hydroelectric power plant.

Principle of generation of hydroelectricity

To generate hydroelectricity from a hydropower plant, water collected in a dam is allowed to
pass through a tunnel. It converts the potential energy of water stored in a dam into kinetic
energy. The force of water can be used to turn turbines connected to the generator to produce

Optional Science - 10 47

PHYSICS

electricity. So kinetic energy of the flowing water is converted into kinetic energy in the
armature of a generator connected to the turbine and finally to the electrical energy. Thus
kinetic energy is converted into electrical energy.

Technology of generation of hydroelectricity

A large volume of water from a source

like river is stored in a dam. Such water

is allowed to fall through a long tunnel

over turbines connected with a generator.

It rotates the armature of the generator

at a high speed. In order to produce an

alternating current of 50 Hz, it is made

to rotate at a speed of 50 revolutions per

second. The rotation of the armature of the fig:Technology of generation of hydroelectricity

generator between two poles of a strong magnet gives rise to electric current, or electricity.

This electricity is transmitted to the sub-stations through a transformer for further distribution

to the houses and factories.

Hydroelectricity as the largest source of renewable energy

Hydroelectricity is the world's most used renewable power source. In 2015, hydropower
generated 16.6% of the world's total electricity and 70% of all renewable electricity and was
expected to increase by about 3.1% each year for the next 25 years. In Nepal, it is estimated that
the total production capacity of hydroelectric power is about 83,000 megawatts (MW). But the
existing hydroelectric power production in Nepal is only 1,232 MW. Pharping Hydro Power,
the first hydropower project, was established in 1911 as Chandrajyoti Hydro-electric power
station by Prime Minister Chandra Shamsher Jang Bahadur Rana.

Know the Reason

Hydroelectricity is the most suitable source of energy in context of our country, why?

In Nepal, there are many fast flowing perennial rivers. These rivers flow from the north
to the south on sloppy land. Such a sloppy land structure is suitable for storing water
in dams. So hydroelectricity is the most suitable source of energy in the context of our
country.

Advantages of hydroelectricity

1. Hydroelectricity does not cause air pollution.
2. It can be transmitted over long distances in extremely small time.
3. It can be converted into different forms of energy, like heat, light, etc. by passing through

suitable devices.
4. Water used to generate hydroelectricity can be reused for other purposes like irrigation.
5. It is cheaper in the long term use though the installation cost of a hydropower plant is

very high.

48 Optional Science - 10

PHYSICS

Limitations of hydroelectricity

1. It results in submersion of extensive areas upstream of the dams.
2. Damming rivers may disrupt wildlife and natural resources.
3. Hydropower stations cannot be sited at a place of our choice.
4. Dams can be very expensive to build.
5. There must be continuous and sufficient flow of water for steady output.
Biofuel: Biogas

Fuels likes wood, biogas, alcohol from the biomass of plants and animals are called biofuels.
Plants trap the sunlight during photosynthesis. Solar energy gets stored in the form of organic
matter in plants. Biomass is any organic matter that can be obtained from living organisms.
For example, wood, crops, dried leaves, seaweed, animal wastes. We use biomass when we eat
plant products or when we burn firewood.

Know the Reason

Biomass is a renewable energy source, why?
Plants and animals will always exist as long as the conditions are suitable for life on the
earth. As long as we plant trees and crops, we will have resources. Biomass supplies
are not limited. It can be obtained continuously on the earth. So biomass is a renewable
energy source.

Biogas: Biomass can be converted into combustible gas, i.e., biogas in a biogas plant. Biogas
is a mixture of gases like methane (CH4), carbon dioxide (CO2), hydrogen (H2) and hydrogen
sulphide (H2S). The major constituent of biogas is methane (65 %).

Memory Plus

Energy released from biomass through combustion or other chemical process is called
biomass energy.

Construction of biogas plant

A biogas plant is a combination of a digester and gas holder, where biogas is produced from

animal dung, human excreta, industrial Slurry ol Cattle , ;=;.,+-- Outftowf0< 8101111
and domestic wastes. In other words, the
biogas plant is the physical installation --Dung &Water -Overflow Tank
to produce biogas from biomass. It is
built either of cement-concrete or bricks. Mbclng Tank
Biogas plant was first introduced to Ground Level
Nepal as an experimental project in

1955. The initial experiences showed the Outiet Chamber
feasibility of this technology for meeting

a significant portion of rural household

energy needs. A biogas plant has the

following components: fig: construction of biogas plant

Optional Science - 10 49

PHYSICS

a. Mixing tank: Feed is fed into the system from a mixing tank. It has a mixing fan to make
slurry from animal dung and water.

b. Inlet Pipe: It is the pipe from the mixing tank to the digestive tank. It is used to send the
feed into the digestive tank.

c. Digestive tank (T): It is a brick-walled underground tank with a dome shaped roof.
A digester is an air-tight tank where the feed and water will stay for some time and
bacterial operation to generate gas will get complete.

d. Dome (gas holder): It stores the biogas generated. With increase in the pressure of the
gas inside the dome, it pushes the digested material out of the tank.

e. Gas outlet: It is a pipe with a valve at the top of the dome. Gas generated is supplied
through an outlet valve. Biogas from the biogas plant can be supplied through pipes for
cooking and lighting.

f. Outlet chamber: It is a rectangular tank on the opposite of the input pipe. The outlet
chamber is for taking out the spent slurry after completion of gas generation from it.

g. Overflow tank: There is an overflow tank over the outlet chamber.

h. Slurry outlet: It is on the overflow tank. Slurry is discharged from the outlet opening.

Input materials for biogas production

The following organically-rich matter is used as input material for biogas production.

a. Animal wastes: Cattle dung, urine, goat and poultry droppings, sericulture wastes,
elephant dung, piggy wastes.

b. Human wastes and kitchen wastes: Human excreta and other kitchen wastes like
chopped vegetables or fruit waste, food gone bad, leftover food. But bony items and other
hard substance should not be added in the mixing tank.

c. Agricultural wastes: Aquatic and terrestrial weeds, crop residues fruit and vegetable
processing wastes, oil cake, etc.

d. Industrial wastes: Sugar factory and paper wastes are industrial wastes that can be
used as input material for biogas production.

In the villages, the main input material for biogas production is cattle dung.

Production of biogas

When cattle dung is used as input material in the mixing tank for biogas production, a slurry
is made from fresh dung and water in the ratio 1:1. This slurry of animal dung and water is
fed into the digester tank. The digester tank is filled with slurry upto the cylindrical level as
shown in the given figure of the biogas plant. Biogas is produced by the breakdown of organic
matter by bacteria in the absence of oxygen. Such bacteria are called anaerobic bacteria.

After installation of the biogas plant, the gas production may take from a few days in summer

to 3- 4 weeks in winter. This biogas starts collecting in the dome. Initially an outlet valve is

kept closed to prevent the produced gas from escaping. After a few days, formation of bubbles

will be noticed in the outlet tank. As more and more biogas collects in the dome, it exerts

pressure on the slurry in the digester tank. The gas is allowed to accumulate till it almost

pushes the slurry to the level of the outlet opening and forces the spent slurry to go into the

overflow tank through the outlet chamber.
050
Optional Science - 10

PHYSICS