CHAPTER 1

Physics Exercises
SP015

Chapter 1 : Physical Quantities And Measurements

At the end of this topic, students should be able to:

1.1 Dimensions of (a) Define dimension.

physical (b) Determine the dimensions of derived quantities.

quantities (c) Verify the homogeneity of equations using dimensional

analysis

1.2 Scalars and (a) Define scalar and vector quantities.

Vectors (b) Resolve vector into two perpendicular components (x and y

axes).

(c) Illustrate unit vectors ( iˆ, ˆj, kˆ ) in Cartesian coordinate.

(d) State the physical meaning of dot (scalar) product;

A • B = AB cos

1.3 Significant (e) State the physical meaning of cross (vector) product;
Figures And
Uncertainty →→
analysis
A B = AB sin nˆ

Note: Direction of cross product is determined by
corkscrew method of right hand rule.
(a) State the significant figures of a given number.
(b) Use the rules for stating the significant figures at the end of
a calculation (addition, subtraction, multiplication or
division)
(c) Determine the uncertainty for average value and
derived quantities
(d) Calculate basic combination (propagation) of uncertainties.
(e) State the sources of uncertainty in the results of an
experiment.
(f) Draw a linear graph and determine its gradient, y-intercept
and its respective uncertainties
(g) Measure and determine the uncertainty of physical
quantities. (Experiment 1: Measurement and
uncertainty)
(h) Write a laboratory report.
(Experiment 1: Measurement and uncertainty)

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Physics Exercises
SP015

STRUCTURED QUESTIONS

1. The orbital radius, r of a satellite revolving around the earth is given by

r3 = GM  T  2
 2 

Where G = 6.67 10−11 Nm2kg-2 , T is the period and M is the mass of the earth.

Determine the homogeneity of this equation.

2. A triangle has side a, b and c. A circle with radius r can be drawn inside the triangle
(a) If r is given by

r= (s − a)(s − b)(s − c) where s = (a + b + c)
s 2

Determine the homogeneity of the expression r.

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(b) If r is multiplied by , will its homogeneity change?

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3.

FIGURE 1

→→ →→

Vector P and Q are shown in FIGURE 1. Determine the component P and Q .

[ Ans: Px=-4.85 m, Qx=4.51 m ,Py=-2.80 m, Qy= 1.64 m ]

4. A girl push a box across the floor and causes it to undergo two displacements A and
B. Displacement A is 1.5 m along the positive x- axis, while displacement B is 1.4 m
along the positive y-axis. Determine the magnitude and direction of the displacement.
[ Ans: R=2.05 m, θ=43.02°]

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Physics Exercises
SP015

5. Given z = xy, where z has the dimension of LM-1 and y has the dimension of LT-1.
Determine the dimension of x. [Ans: T M-1]

6. The gravitational acceleration, ag of an object on Earth is given by the equation,

ag = GM , where M and r is the mass and radius of Earth respectively. Determine
r2

the dimension of the constant G.

[Ans: L3 T-2 M-1]

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