TOM Objective

THEORY OF MACHINE

THEORY OF MACHINES (Objective)

CONTENTS

Unit Chapters Page No.
1 Mechanisms, Velocity & Acceleration 2 - 20
2 Gears 21- 33
3 Flywheel 34 - 37
4 Vibration 38 - 58
5 Governors 59 - 66

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Rajnandgaon (Chhattisgarh) Mob : 09993336391

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MECHANICAL ENGINEERING

1 MECHANISMS, VELOCITYAND ACCELERATION

Class Room Objective

1 The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is .

(ME-05)

(a) 1 (b) 2 (c) 3 (d) 4

Common data for Q2.Q3, and Q 4

An instantaneous configuration of a four bar mechanism, whose plane is horizontal is shown in the fig
below. At this instant, the angular velocity and angular acceleration of link O2A are = 8 rad/s and = 0,
respectively, and the driving torque () is zero. The link O2Ais balanced so that its center of mass falls at O2

B
260

100

A 60mm 160mm

 90o 90o
O4
 240mm


O2

2 Which kind of 4 - bar mechanism is O2ABO4 ? (ME-05)

(a) Double crank mechanism (b) Crank-rocker mechanism

(c) Double-rocker mechanism (d) Parallelogram mechanism

3 At the instant considered, what is the magnitude of the angular velocity of O4B ? (ME-05)

(a) 1 rad / s (b) 3 rad / s

(c) 8 rad / s (d) 64 / 3 rad / s

4 At the same instant, if the component of the force at jointAalongAB is 30 N, then the magnitude of the

joint reaction at O2.(ME-05) (b) is 30 N
(a) is zero

(c) is 78 N (d) cannot be determined from the given data

5 In the fig shown, the relative velocity of link 1 with respect to link 2 is 12 m/sec. Link 2 rotates at a

constant speed of 120 rpm. the magnitude of Coriolis component of acceleration of link 1 is.(ME-04)

(a) 302 m/s2. 2
(b) 604 m/s2. 1
(c) 9.6 m/s2.
(d) 1208 m/s2.

2

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THEORY OF MACHINE

6 The fig below shows a planar mechanism with single degree of freedom. (ME-04)

1 2L N

3 4
90o M

1

The instant center 24 for the given configuration is located at a position.

(a) L (b) M (c) N (d) 

7 Match the following:- (ME-04)

Type of Mechanism Motion achieved

P. Scott-Russel mechanism - 1. Intermittent motion

Q. Geneva mechanism - 2. Quick return motion

R. Off-set slider-crank mechanism - 3. Simple harmonic motion

S. ScotchYoke mechanism - 4. Straight line motion

Codes:-

P QRS

(a) 2 3 1 4

(b) 3 2 4 1

(c) 4 1 2 3

(d) 4 3 1 2

8 Match the following with respect to spatial mechanisms. (ME-04)

Type of joint Degrees of Constraint

P - Revolute - 1. Three

Q - Cylindrical - 2. Five

R - Spherical - 3. Four

- 4. Two

- 5. Zero

Codes:

P QR

(a) 1 3 5

(b) 5 4 3

(c) 2 3 1

(d) 4 5 3

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MECHANICAL ENGINEERING

9 In the linkage shown in fig, O1A= 50 mm,AB = 60 mm, O2B = 50 mm, BC = 50 mm, CD = 60 mm,
O3D = 100 mm. In the position shown in the fig, if O1A has momentarily an angular veloctiy of
2 rad/s with out any angular acceleration, then the velocity and acceleration of D will be: (ME-04)

D C O1

(a) 100 mm/s, 100 mm/s2.

(b) 200 mm/s, 100 mm/s2. BA
(c) 200 mm/s, 300 mm/s2. O3 O2
(d) 200 mm/s, 400 mm/s2.

10 Inversions of a mechanism can be obtained by. (PI-03’ )

(a) adding more links (b) changing itslink lengths

(c) fixing itsdifferent links (d) changing link positions/ orientations

Data for Q11 & Q12 are given below. Solve the problems and choose correct answers.
The circular disc shown in its plan view in the fig. rotates in a plane parallel to the horizontal plane about
the point O at a uniform angular velocity . Two other pointsAand B are located on the line OZ at distances

rA and rB from O respectively.

11 The velocity of point B with respect to point Ais a vector of magnitude . (ME-03)
(A) 0
(B)  ( rB- rA) and direction opposite to the direction of motion of point B
(C)  ( rB- rA) and direction same as the direction of motion of point B
(D)  ( rB- rA) and direction being from O to Z.

Z

B

A

O

12 The acceleration of point B with respect to point Ais a vector of magnitude. (ME-03)

(A) 0
(B)  ( rB2- rA2) and direction same as the direction of motion of point B
(C) 2 ( rB- rA) and direction opposite to the direction of motion of point B
(D) 2 ( rB- rA) and direction being from Z to O.

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THEORY OF MACHINE

13 The minimum number of links in a single degre-of-freedom planar mechanism with both higher and

lower kinematic pairs is. (ME-02)

(a) 2 (b) 3 (c) 4 (d) 5

14 The Coriolis component of acceleration is present in. (ME-02)

(a) 4-bar mechanisms with 4 turning pairs (b) shaper mechanism

(c) slider crank mechanism (d) ScotchYoke mechanism

15 In a single degree-of-freedom, 4-link, revolute jointed Grashoff mechanism,’l’is the longest link,’s’is

the shortest link and p,q are the two remaining links. These links may be in any order. (ME-02)

(a) write down the condition for feasibilityof Grashoff mechanism.

(b) When will you get crank - crank, crank rocker and rocker - rocker type of mechanisms by fixing

links s,l,p or q respectively.

(c) Draw these mechanisms showing motions of crank and rocker links.

16 A four bar mechanism ABCD is shown in the given fig. If the linear velocity ‘V’of the point ‘B’ is

0.5 m/s, then the linear velocity ‘V’ of point ‘C’ will be.

(a) 1.25 m/s E.............0. 1 m
(b) 0.5 m/s 
(c) 0.4 m/s VB 0. 25 m C
(d) 0.2 m/s
B VC D
A =30o

17 Instantaneous center of a body rolling with sliding on a staitonary curved surface lies .
(a) at the point of contact.
(b) on the common normal at the point of contact
(c) on the common tangent at the point of contact
(d) at the center of curvature of the stationary surface

18 The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in

the fig. is (93)

(a) 3

(b) 4 4 3
(c) 2 5
(d) 1 2
1

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MECHANICAL ENGINEERING

19 Fig. shows a quick return mechanism. The cranks OA rotates clockwise uniformly. OA 2 cm,
OO1 = 4cm. The ratio of time for forward motion to that for return motion is. (95)

B

(a) 0.5 2 ----------------A
(b) 2.0 O

(c) 12 4
(d) 1 O

20 Arod of length 1 m is sliding in a corner as shown in fig.At an instant when the rod makes an angle of
60o with the horizontal plane, the velocity of point ‘A’on the rod is 1 m/s. The angular velocity of the

rod at this instant is . (96)

(a) 2 rad/s



(b) 1.5 rad/s  
(c) 0.5 rad/s
(d) 0.75 rad/s A 1m

6 0o
B

21 The number of inversions for a slider crank mechanism is

(a) 6 (b) 5 (c) 4 (d) 3

22 Match the items in columns I and II. (ME-06)

Column I Column II

P. Addendum - 1. Cam

Q. Instantaneous center of velocity - 2. Beam

R. Section modulus - 3. Linkage

S. Prime circle - 4. Gear

Codes:-

P QRS

(a) 4 2 3 1

(b) 4 3 2 1

(c) 3 2 1 4

(d) 3 4 1 2

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THEORY OF MACHINE

23 Match the items in columns I and II (ME-06)

Column I Column II

P. Higher kinematic pair - 1. Grubler’s equation

Q. Lower kinematic pair - 2. Line contact

R. Quick return mechanism - 3. Euler’s equation

S. Mobilityof a linkage - 4. Planer

- 5. Shaper

- 6. Surface contact

Codes:-

P QRS P QRS

(a) 2 6 4 3 (b) 6 2 4 1

(c) 6 2 5 3 (d) 2 6 5 1

24 In a four - bar linkage, S denotes the shortest link length, L is the longest link length, P and Q are the

lengths of other two links.At least one of the three moving links will rotate by 360o if. (ME-06)

(a) S + L  P + Q (b) S + L  P + Q (c) S + P  L + Q (d) S + P > L + Q

25 The input link OP of a four bar linkage is rotated at 2 rad/s counter clockwise direction as shown
below. the angular velocity of the coupler PQ in rad/s, at an instant when O4O2P = 180o , is

(ME =07 )

(a) 4 Q

(b) 2 2 P PQ=O4Q = 2 a
(c) 1 O2
(d) 1 / 2 O2P=O2Q4 = a

O4

26 If the quick return ratio is 1 : 2 then the length of the crank in mm is . (ME-07)

(a) 250 R Q
(b) 250 3  = 2 rad/s S
(c) 500
(d) 500  3 O<>
500 mm

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MECHANICAL ENGINEERING

27 The angular speed o PQ in rad/s when the block R attains maximum speed during forward stroke

(stroke with slower speed ) is . (ME-07)

(a) 1/3 (b) 2 / 3 (c) 2 (d) 3

28 A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mecha

nism, using Grubler’s criterion, is (ME - 08)

(a) 0 (b) 1 (c) 2 (d) 3

29 Acircular disk of radius ‘R’rolls without slipping at a velocity v. The magnitude of the velocityat point

‘P’ (see fig.) is (ME-08)

3P0o
----------------------------------
--------R----------------- v 

30. For a four - bar linkage in toggle position, the valve of

mechanical advantage is (ME-06)

a) 0.0 b) 0.5 c) 1.0 d) 

Practice Questions :

31 Scoth yoke mechanism is used to generate

(a) sine functions (b) square roots (c) logarithms (d) inversions

32 Inversion of a mechanism is

(a) changing of a higher pair to lower pair.

(b) obtained byfixing different links in a kinematic chain

(c) turning it upside down

(d) obtained by reversing the input and output motion.

33 The sense of Coriolis component 2 Vw is the same as that of the relative velocity vector V rotated.
(a) 45o in the direction of rotation of the link containing the path.
(b) 45o in the direction opposite to the rotation of the link containing the path.

(c) 90o in the direction of rotation of the link containing the path.
(d) 180o in the direction opposite to the rotation of the linkcontaining the path.

34 Consider the following statements :

Coriolis component of acceleration depends on

1. Velocity of slider 2. angular velocityof the link

3. acceleration of slider 4. angular acceleration of link

Of these statements

(a) 1 and 2 are correct (b) 1 and 3 are correct

(c) 2 and 4 are correct (d) 1 and 4 are correct

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THEORY OF MACHINE

35 ABCD is a four - bar mechanism in which AB = 30 cm and CD = 45 cm. AB and CD are both
perpendicular to fixed linkAD, as shown in the fig. If velocity of B at this condition is V, then velocity of
C is.

C

(a) V B 45
(b) (3/2) V 30
(c) (9/4) V
(d) (2/3) V

AD

36 Match list - I with list - II and select the correct answer using the codes given below the lists:

List - I List - II

A. Quadric cycle chain - 1. Elliptic trammel

B. Single slider crank chain - 2. Rapsons slide

C. Double slider crank chain - 3.Ackerman steering

D. Crossed slider crank chain - 4. Eccentric mechanism

5. Pendulum pump

Codes:
ABCD

(a) 5 4 2 1
(b) 3 1 5 4
(c) 5 3 4 2
(d) 3 5 1 2

37 The Klein’s method of construction for reciprocating engine mechanism.
(a) is a simplified version fo instantaneous centre method.
(b) utilizes a quadrilateral similar to the diagram of mechanism for reciprocating engine.
(c) enables determination of Corialli’s component
(d) is based on the acceleration diagram

38 The instantaneous centre of rotation of a rigid thin disc
rolling on a plane rigid surface is located at .
(a) the centre of the disc
(b) an infinite distance on the plane surface
(c) the point of contact
(d) the point of the circumference situated vertically opposite to the contact point.

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MECHANICAL ENGINEERING

39 The direction of Coriolis component of acceleration 2 V, of the sliderAwith respect to the coincident
point B is shown in fig. 1,2,3 and 4. Directions shown by fig.

(a) 2 and 4 are wrong 
(b) 1 and 2 are wrong V  V  
(c) 1 and 3 are wrong 2V
(d) 2 and 3 are wrong 2V B2V B B 2VB
A AA A


 V  V 

O OO O

40 Which one of the following is an Open pair ?
(a) Ball and socket joint
(b) Journal bearing
(c) Lead screw and nut
(d) Cam and follower

41 In the mechanism ABCD shown in the given fig, the fixed link is denoted as (1), Crank AB as (2),
rocker BD as (3). Swivel trunnion at C as (4) The instantaneous centre I41 is at.

D C
4

B3

21

A

(a) the centre of swivel trunnion
(b) the intersection of lineAB and a perpendicular to BD
(c) infinityalongAC
(d) infinityperpendicular to BD

42 In order to draw acceleration diagram, it is necessary to determine the Coriolis component of
acceleration in the case of.
(a) crank and slotted lever quick return mechanism
(b) slider - crank mechanism
(c) four bar mechanism
(d) pantograph

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THEORY OF MACHINE

43 Match list - I (Positioning of two shafts) with list - II (Possible connection) and select the correct

answer using the codes given below the lists :

List - I List - II

A. Parallel shafts with a slight offset - 1. Hookes joint

B. Parallel shafts at a reasonable distance - 2. Worm and wheel

C. Perpendicular shafts - 3. Oldham coupling

D. Intersecting shafts - 4. Belt and pulley

Codes :

ABCD

(a) 4 3 2 1

(b) 4 3 1 2

(c) 3 4 1 2

(d) 3 4 2 1

44 When a slider moves with a velocity ‘V’ on a link rotating at an angular speed of ,the Corioli’s

component of acceleration is given by.

(a) 2 V. (b) V. (c) V/ 2 (d) 2 V

45 The total number of instantaneous centres for a mechanism consisting of ‘n’ links is

(a) n/2 (b) n (c) (n-1)/2 (c) n (n-1) / 2

46 Which of the following pairs are correctly matched ? Select the correct answer using the codes given

below the pairs.

Mechanism Chain from which derived

1. Whitworth quick return motion 1. Single slider crank chain

2. Oldham’s coupling 2. Four bar chain

3. Scotch Yoke 3. Double slider crank chain

Codes :

(a) 1 and 2 (b) 1,2 and 3

(c) 1 and 3 (d) 2 and 3

47 Match list - I with list - II and select the correct answer using the codes given below the lists:

List - I List - II

A. 4 links, 4 turning pairs 1. Complete constraint

B. 3 links, 3 turning pairs 2. Successful constraint

C. 5 links, 5 turning pairs 3. Rigid frame

D. Footstep bearing 4. Incomplete constraint

Codes :

ABCD

(a) 3 1 4 2

(b) 1 3 2 4

(c) 3 1 2 4

(d) 1 3 4 2

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MECHANICAL ENGINEERING

48 Consider a four- bar mechanism shown in the given fig. The driving link DA is rotating uniformly at a
speed of 100 rpm clockwise . the velocity of Awill be.

(a) 300 cm/s A 36 cm B
(b) 314 cm/s 60 cm 36 cm
(c) 325 cm/s 
(d) 400 cm/s C
30 cm
60o

D

49 Which one of the following pairs is correctly matched ?
(a) Governors........... Interference
(b) Gears ............. Hunting
(c) Klein’s construction .........Acceleration of piston
(d) Cam ................ Pinion

50 In a single slider four - bar linkage, when the slider is fixed, it forms a mechanism of
(a) hand pump
(b) reciprocating engine
(c) quick return
(d) oscilating cylinder

51 The kinematic chain shown in the fig. is a .

(a) Structure

(b) mechanism with one degree of freedom

(c) mechanism with two degrees of freedom

(d) mecahnism with more than two degrees of freedom

52 A point on a link connecting a double slider crank chain will trace a.

(a) straight line (b) circle

(c) parbola (d) ellipse

53 Consider the following pairs of parts :

1. Pair of gear in mesh.

2. Belt and pulley

3. Cylinder and piston

4. cam and follower

Among these, the higher pairs are

(a) 1 and 4 (b) 2 and 4

(c) 1, 2 and 3 (d) 1, 2 and 4

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THEORY OF MACHINE

54 Consider the following statements:

1. Round bar in a round hole forms a turning pair.

2. Asquare bar in a square hole forms a sliding pair.

3.Avertical shaft in a foot - step bearing forms a successful constraint.

Which of these statements are correct ?

(a) 1 and 3 (b) 1 and 2

(c) 2 and 3 (d) 1, 2 and 3

55 A four - bar chain has

(a) all turning pairs.

(b) one turning pair and the others are sliding pairs.

(c) one sliding pair and the others turning pairs.

(d) all sliding pairs.

56 Match list I with list II and select the correct answer using the codes given below the lists:

List - I List - II

A. Compound train - 1. Hart mechanism

B. Quick return mechanism - 2. Coriolis force

C. Exact straight line motion - 3. Transmission of motion around bends and corners

D.Approximate straight line motion- 4. Watt mechanism.

Codes :

ABCD

(a) 1 2 3 4

(b) 3 2 1 4

(c) 3 4 1 2

(d) 1 4 3 2

57 Match list - I (Kinematic inversions) with List - II (Applications) and select the correct answer using the

codes given below the lists:

List - I List - II

A. - 1. Hand pump
B. - 2. Compressor

C. - 3. Whitworth quick return mechanism

D. - 4. Oscillating Cylinder Engine

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MECHANICAL ENGINEERING

Codes :
ABCD
(a) 1 3 4 2
(b) 2 4 3 1
(c) 2 3 4 1
(d) 1 4 3 2

58 Assertion (A) : The elements of higher pairs must be force closed.
Reason (R) : This is requiredin order toprovide completely constrained motion

Previous IES Questions for Practice :

1 Match list - I with list - II and select the correct answer using the codes given below the lists:

List - I List - II

A. Crank shaft - 1. Supports the revolving part and transmits torque.

B. Wire shaft - 2. Transmits motion between shafts where it is not possible to effect a

rigid coupling between them.

C. Axle - 3. Converts linear motion into rotary motion.

D. Plain shaft - 4. Supports only the revolving parts.

Codes:-

ABCD

(a) 3 2 1 4

(b) 4 2 3 1

(c) 3 2 4 1

(d) 1 4 2 3

Direction:- The following items consist of two statements, one labelled theAssertion (A) and the other

labelled the Reason (R). You are to examine these two statements carefully and decide if theAssertion (A)

and the Reason (R) are individually true and if so, whether the Reason is a correct explanation of the

Assertion. Select your answer to these items using the codes given below and mark your answer sheet

accordingly.

Codes:
(a) BothAand R are individually true and R is the correct explanation ofA.
(b) BothAand R are individually true but R is not the correct explanation of A.
(c) Ais true but R is false.
(d) Ais false but R is true.
2 Assertion (A): Hydraulic fluid is one form a link.
Reason (R): A link need not necessarily be a rigid body but it must be a resistant body.
3 Assertion (A): TheAckermann steering gear is commonly used in all automobiles.
Reason (R): It has the correct inner turning angle q for all questions.

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THEORY OF MACHINE

4 In a slider crank mechanism, the maximum acceleration of slider is obtained when the crank is.

(a) at the inner dead centre position.

(b) at the outer dead centre position.

(c) exactly midway position between the two dead centres two dead centres.

(d) None of these.

5 Match list - I with list - II and select the correct answer:

List - I List - II

A. Cam and follower - 1. Grubler’s rule.

B. Screw pair - 2. Grashoff’s linkage.

C. 4-bar mechanism - 3. Pressure angle.

D. Degree of freedom - 4. Single degree of freedom.

of planar mechanism

Codes:

ABCD

(a) 3 4 2 1

(b) 1 2 4 3

(c) 1 4 2 3

(d) 3 2 4 1

6 Match list - I (Kinematic pairs) with List - II (Practical example) and select the correct answer:

List - I List - II

A. Sliding pair - 1.Aroad roller rolling over the ground.

B. Revolute pair - 2. Crank shaft in a journal bearing in an engine.

C. Rolling pair - 3. Ball and socket joint.

D. Spherical pair - 4. Piston and cylinder.

- 5. Nut and screw.

Codes :

ABCD

(a) 5 2 4 3

(b) 4 3 1 2

(c) 5 3 4 2

(d) 4 2 1 3

7 Match list - I (Mechanism) with list - II (Motion) and select the correct answer:

List - I List - II

A. Hart mechanism - 1. Quick return motion.

B. Pantograph - 2. Copying mechanism.

C. Whitworth mechanism - 3. Exact straight line motion.

D. Scotch yoke - 4. Simple harmonic motion.

- 5.Approximate straight line motion.

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 MECHANICAL ENGINEERING

Codes:
ABCD

(a) 5 1 2 3
(b) 3 2 1 4
(c) 5 2 1 3
(d) 3 1 2 4

8 The crank and slotted lever quick - return motion mechanism is shown in fig. The length of links
O1,O2,O1 C and O2 A are 10 cm, 20 cm and 5cm respectively.

C

A
O2

O1

The quick return ratio of the mechanism is .
(a) 3.0
(b) 2.75
(c) 2.5
(d) 2.0

9 f = 3 (n-1) -2j. In the Grubler’s equation for planer mechanisms given. j is the
(a) Number of mobile links
(b) Number of links
(c) Number of lower pairs
(d) Length of the longest of the longest link.

10 In a slider - crank mechanism, the velocity of piston becomes maximum when.
(a) Crank and connection rod are in line with each other.
(b) Crank is perpendicular to the line of stroke of the piston.
(c) Crank and connecting rod are mutually perpendicular.
(d) Crank is 120o with the line of stroke.

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THEORY OF MACHINE

11 Three positions of the quick-return mechanism are shown below. In which of the cases does the

Coriolis component of acceleration exist?

Select the correct answer using the codes given below: R

RR Q

QQ

P 90o P P

O OO

(1) (2) (3)

(a) 1 only (b) 1 and 2 (c) 1, 2 and 3 (d) 2 and 3

12 Which of the mechanisms shown above do/does not have single degree of freedom ?

(1)
(1)

(3) (4)

(a) 3 and 4 (b) 2 and 3 (c) 3 only (d) 4 only.

13 In the diagram given below, the magnitude of absolute angular velocity of link 2 is 10 radians per

second while that of link 3 is 6 radians per second.What is the angular velocity of link 3 relative to 2?

3
2

 4

45o 1
D

(a) 6 radians per second (b) 16 radians per second
(c) 4 radians per second (d) 14 radians per second

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MECHANICAL ENGINEERING

14 In the fig given above, the link 2 rotates at an angular velocity of 2 rad/s. What is the magnitude of

Corolis acceleration experienced by the link 4 ? (05)

30 cm 1
300

42

3

40 cm 300

(a) 0 (b) 0.8 (c) 0.24 m/s2 (d) 0.32 m/s2.

15 Consider the following statements: (05)

1. The degree of freedom for lower kinematic pairs is always equal to one.

2. A ball - and - socket joint has 3 degrees of freedom and is a higher kinematic pair.

3. Oldham’s coupling mechanism has two prismatic pairs and two revolute pairs.

Which one of the statements given above is / are correct?

(a) 1, 2 and 3 (b) 1 only

(c) 2 and 3 (d) 3 only

16 In a Kinematic chain, a quaternary joint is equivalent to: (05)

(a) One binary joint (b) Two binary joint

(c) Three binary joint (d) Four binary joint

17 B (06)

A

Assertion (A): LinkAexperiences Coriolis acceleration relative to the fixed link.
Reason (R) : Slotted link Ais rotating with angular velocity w and the Block slides in the slot ofA.
(a) Both Aand R are true and R is the correct explanation of A.
(b) BothA and R are individually true but R is not the correct explanation ofA.
(c) A is true but R is false.
(d) A is false but R is true.

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THEORY OF MACHINE

18 Consider the following statements: (06)

1. Lower pairs are more resistant than the higher pairs in a plane mechanism.

2. In a 4-bar mechanism (with 4 turning pairs), when the link opposite to the shortest link is fixed, a

double rocker mechanism results. (06)

Which of the statements given above is / are correct?

(a) 1 only (b) 2 only

(c) Both 1 and 2 (d) Neither 1 nor 2

19 What is the number of instantaneous centres of rotation for a 6- link mechanism ? (06)

(a) 4 (b) 6 (c) 12 (d) 15

20 What is the direction of the Coriolis component of acceleration in a slotted lever crank mechanism ?

(07)

(a)Along the sliding velocity vector.

(b)Along the direction of the crank.
(c) Along a line rotated 90o from the sliding velocity vector in a direction opposite to the angular

velocity of the slotted lever.
(d) Along a line rotated 90o from the sliding velocity vector in a direction same as that of the angular

velocity of the slotted lever.

21 In a slider - bar mechanism, when does the connecting rod have zero angular velocity ? (07)

(a) When crank angle = 0o (b) When crank angle = 90o

(c) When crank angle = 45o (d) Never

22 Match list - I (Principle / Method) with list - II (Corresponding Application) and select the correct

answer using the code given below the lists: (08)

List - I List - II

A. Klein’s construction - 1. Instantaneous centers in linkages

B. Kennedy’s theorem - 2. Relative acceleration of linkages.

C. D’Alembert’s principle - 3. Mobilityof linkages.

D. Grubler’s rule - 4. Dynamic forces in linkages.

Codes:

ABCD

(a) 4 1 2 3

(b) 2 3 4 1

(c) 4 3 2 1

(d) 2 1 4 3

23 Which mechanism produces intermittent rotary motion from continuous rotary motion ? (08)

(a) Whitworth mechanism

(b) Scotch yoke mechanism

(c) Geneva mechanism

(d) Elliptical trammel.

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MECHANICAL ENGINEERING

24 Which one of the following mechanism represents an inversion of the single slider crank chain ?
(a) Elliptical trammel
(b) Oldham’s coupling
(c) Whitworth quick return mechanism
(d) Pantograph mechanism.
*******

“If you thank you can win, you can win.
Faith is necessary to victory”

Class Room Objectives
1-c, 2-b, 3-b, 4-b, 5-a, 6-d, 7-c, 8-c, 9-d, 10-c, 11-c, 12-d, 13-b, 14-b, 15-?, 16-d, 17-b, 18-c, 19-b,
20-?, 21-c, 22-b, 23-d, 24-a, 25-c, 26-a, 27-b, 28-b, 29-a, 30-d.
Practice Questions
31-a, 32-b, 33-c, 34-a, 35-a, 36-d, 37-b, 38-c, 39-a, 40-d, 41-a, 42-a, 43-d, 44-d, 45-d, 46-c, 47-d,
48-b, 49-c, 50-a, 51-b, 52-d, 53-d, 54-d, 55-a, 56-b, 57-c, 58-A
Previous IES Questions for Practice :-
1-c, 2-A, 3-c, 4-a, 5-a, 6-d, 7-b, 8-d, 9-c, 10-b, 11-a, 12-d, 13-c, 14-a, 15-a, 16-c, 17-d, 18-c, 19-d,
20-d, 21-b, 22-d, 23-c, 24-c.

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THEORY OF MACHINE

2 GEARS

Class Room Objective :
Data for Q 1 and 2 are given below. Solve the probelms and choose correct answers
A compacting machine shown in the figure below is used to create a desired thrust force by using a rack

and pinion arrangement. The input gear in mounted on the motor shaft. The gears have involve teeth of 2 mm
module. (GATE-04)

========= 1000 N

 RACK

T = 80 =========T = 80

-------

T = 20

MOTOR

1. If the drive efficiency is 80%, the torque required on the input shaft to create 1000 N output thurst is

a) 20 Nm b) 25 Nm c) 32 Nm d) 50 Nm

2. If the pressure angle of the rack is 200, the force acting along

the line of action between the rack and the gear teeth is

a) 250 N b) 342 N c) 532 N d) 600 N

3. Match the items in column I and II (GATE-06)

Column I Column II

P. Addendium 1. Cam

Q. Instantaneous center of velocity 2. Beam

R. Section modulus 3. Linkage

S. Prime circle 4. Gear

a) P-4, Q-2, R-3, S-1

b) P-4, Q-3, R-2, S-1

c) P-3, Q-2, R- 1, S-4

d) P-3, Q-4, R-1, S-2

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MECHANICAL ENGINEERING

Common Data for Questions 4 and 5

A planetary gear train has four gears and one carrier. Angular velocities of the gears 1, 2,  and 4,
3
respectively. The carrier rotates with angular velcity 5.
(GATE-06)

Gear 2 ``’’ Gear 3
45T 20T

------ - - - - -
- - - - -

Gear 1 Carrier 5
15T
Gear 4
40T

4. What is the relation between the angular velocities of Gear 1 and Gear 4 ?

 -   - 
1 5 4 5
a) = 6 b)  -  = 6
 -
45 15

c)  -  2 d)  -  8
12 25
=- =
 - 3  - 9
45 45

5. For  = 60 rpm clockwise (cw) when looked from the left, what is the angujlar velocity of the carrier
1

its direction so that Gear 4 rotates in counterclockwise (ccw) direction at twice the angular velocity of

Gear 1 when looked from the left ?

a) 130 rpm, cw b) 223 rpm, ccw

c) 256 rpm, cw d) 156 rpm, ccw

6. An epicylic gear train is shown schematically in the adjacent figure. The sun gear 2 on the input shaft is

a 20 teeth external gear. The planet gear 3 is a 40 teeth external gear. The ring gear 5 is a 100 teeth

internal gear. The ring gear 5 is fixed and the gear 2 is rotating at 60 rpm ccw (ccw = counter -

clockwise and cw = clockwise) (GATE-09)

3 4
52

The arm 4 attached to the output shaft will rotate at

a) 10 rpm ccw b) 10 rpm cw

c) 12 rpm cw d) 12 rpm ccw

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THEORY OF MACHINE

Data for Q. 7 & 8 are given below. Solve the problems and choose correct answers .

The overall ratio in a 2 stage speed reduction gear box (with all spur gears) is 12. The input and output

shafts of the gear box are collinear. The countershaft which is parallel to the input and output shafts has a

gear (Z teeth) and pinion (Z = 15 teeth) to mesh with pinion (Z = 16 teeth) on the input shaft and gear (Z
23 1 4

teeth) on the output shaft respectively. It was decided to use a gear ratio of 4 with 3 module in the first stage

and 4 module in the second stage. (GATE-03)

7. Z2 and Z4 are b) 45 and 64
a) 64 and 45

c) 48 and 60 d) 60 and 48

8. The centre distance in the second stage is

a) 90 mm b) 120 mm

c) 160 mm d) 240 mm

9. Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and trans

mits a torque of 20 N.m. The torque transmitted by gear is (GATE-04)

a) 6.6 Nm b) 20 Nm

c) 40 Nm d) 60 Nm

10. Match the following

Type of gears Arrangement of shafts

P. Bevel gears 1. Non-parallel off-set shafts

Q. Worm gears 2. Non-parallel intersecting shafts

R. Herringbone gear 3. Non-parrel, non-intersecting shafts

S. Hypoid gears 4. Parallel shafts

a) P - 4, Q - 2, R - 1, S - 3

b) P - 2, Q - 3, R- 4, S - 1

c) P - 3, Q - 2, R - 1, S- 4

d) P - 1, Q - 3, R - 4, S - 2

11. Twenty degree full depth involute profiled 19-tooth pinion and 37-tooth gear are in mesh. If the module

is 5mm, the center distance between the gear pair will be (GATE-06)

a) 140 mm b) 150 mm

c) 280 mm d) 300 mm

Statement for Linked Answer Questions 12 to 14 :

A gear set has a pinion with 20 teeth and a gear with 40 teeth. The pinion runs at 30 rev/s and transmits

a power of 20 kW. The teeth are on the 200 full-depth system and have a module of 5 mm. The length of the

line of action is 19 mm (GATE - 07)

12. The center distance for the above gear set in mm is

a) 140 b) 150 c) 160 d) 170

13. The contact ratio of the contacting tooth is

a) 1.21 b) 1.25 c) 1.29 d) 1.33

14. The resultant force on the contacting gear tooth is N is

a) 77.23 b) 212.20 c) 2258.1 d) 289.43

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MECHANICAL ENGINEERING

15. A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of

200. It is transmitting a power of 3kW at 20 rev/s. Taking a velocity factor of 1.5 and a form factor of 0.3,

the stress in the gear tooth is about (GATE-08)

a) 32 MPa b) 46 MPa c) 28 MPa d) 70 MPa
(GATE-08)
16. Match the type of gears with their most appropriate description

Type of gear Description

P. Helical 1.Axes non parallel and non intersecting

Q. Spiral Bevel 2.Axes parallel and teeth the inclined to the axis

R. Hypoid 3.Axes parallel and teeth and parallel to the axis

S. Rack and pinion 4.Axes are perpendiular and intersecting and teeth are inclined to the axis

5. Axes are perpendicular and used for large speed reduction

6.Axes parallel and one of the gears has infinite radius

a) P-2, Q-4, R-1, S-6 b) P-1, Q-4, R-5, S-6

c) P-2, Q-6, R-4, S-2 d) P-6, Q-3, R-1, S-5

17. On tooth of a gear having 4 module and 32 teeth is shown in the figure.Assume that the gear tooth and

the corresponding tooth space make equal intercepts on the pitch circumference. The dimensions ‘a’ and ‘b’

respectively, are closest to (GATE-08)

a
<>

Pitch circle <>b

a) 6.08 mm, 4 mm b) 6.48 mm, 4.2 mm

c) 6.28 mm, 4.3 mm d) 6.28 mm, 4.1 mm

Statement for Linked Answer Questions 18 & 19 :

A 200 full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its

face width is 25 mm. (GATE-09)

18. The trangential force transmitted (in N) is

a) 3552 b) 2611 c) 1776 d) 1305

19. Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factors

intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is

a) 242.0 b) 166.5 c) 121.0 d) 74.0

***********

(Ans.)

1 - b, 2 - c, 3 - b, 4 - a, 5 - d, 6 - a, 7 - a, 8 - b, 9 - d, 10 - b, 11 - a, 12 - b, 13 - c, 14 - c, 15 - c,

16 - a, 17 - d, 18 - a, 19 - b.

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THEORY OF MACHINE

Pactice Objectives:
1 A torsional system with discs of moment of inertia l1and l2 , shown in the given fig, is gear driven such

that the ratio of the speed of shaft B to shaft A is ‘n’. Neglecting the inertia of gears, the equivalent
inertia of disc of B at the speed of shaft Ais equal to.

(a) nl2. I1 A
(b) n2l2.
(c) l2/n2. I2
(d) l2/n. B

2 Which one of the following is true for involute gears ?
(a) Interference is inherently absent.
(b) Variation in centre distance of shaft increases radial force.
(c)Aconvex flank is always in contact with concave flank.
(d) pressure angle is constant through the teeth engagement

3 The gear train usually employed in clocks is a
(a) reverted gear train.
(b) simle gear train
(c) sun and planet gear
(d) differential gear.

4 Which of the following statements are correct?
1. For constant velocity ratio transmission between two gears , the common normal at the point of
constant must always pass through a fixed point on the line joining the centres of rotation of the gears.

2. For involute gears the pressure angle changes with change in centre distance between gear.

3. The velocity of ratio compound gear train depends upon the number of teeth the input and output gears

only.

4. Epicyclic gear trains involve rotation of at least one gear exit about some other gear axis.

(a) 1,2 and 3 (b) 1 and 3

(c) 1,2 and 4 (d) 2,3 and 4

5 Two geared shaftAand B having moments of inertia la and lb angular acceleration a and b respecitvely
are meshed to gather.Brotates at G times the speed ofA. If the gearing efficiency of the two shafts in
 then in order to accelerate B, the torque which must be applied toA will be.

(a) 1aa+ G2l bb /. (b) G2l ba .
(c) G2la a . (d) G2lb b .

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MECHANICAL ENGINEERING

6 Cosider the following characteristics:

A. Small interference. B. Strong tooth

C. low production cost D. Gear with small number of teeth.

These characteristics which are aplicable to stub 20o involute system would include.

(a) 1 only (b) 2 ,3 only 4

(c) 1, 2 and 3 (d) 1, 2, 3 and 4

7 Consider the following statements regarding the choice of

conjugate teeth for the profiles of mating gears:

1. They will transmit the desired motion.

2. They are difficult to manufacture.

3. Standardization is not possible.

4. The cost of production is low.

Which of these statements are correct ?

(a) 1 , 2 and 3 (b) 1,2 and 4

(c) 2, 3 and 4 (d) 1,3 and 4

8 The speed ratio in the case of compound train of wheels is equal to.

(a) No. of teeth on first driver (b) No. of teeth on last follower

No. of teeth on last follower No. of teeth on first driver

Product of teeth on the drivers (d) Product of teeth on the follower
Product of teeth on the drivers
(c) Product of teeth on the follower
2. Belt and pulley
9 Consider the following pairs of parts: 4. Cam and follower
1. Pair of gear in mesh
3. Cylinder and piston (b) 2 and 4
Among these, the higher pairs are (d) 1, 2 and 4
(a) 1 and 4
(c) 1, 2 and 3

10 Assertion (A): Helical gears are used for transmitting motion and power between intersecting shafts,
where as straight bevel gears are used for transmitting motion and power between two shafts intersecting
each other at 90o.

Reason (R): In helical gears teeth are inclined to the axis of the shaft and are in the form of a helix,
whereas in bevel gears, teeth are tapered both in thickness and height from one end to the other.

(a) BothAand R are individually true and R is the correct explanation ofA.
(b) Both Aand R are individually true but R is not the correct explanation ofA.
(c) Ais true but R is false.
(d) Ais false but R is true.

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THEORY OF MACHINE

11 In a simple gear train, if the number of idler gears is odd, the direction of motion of driven gear will.

(a) be same as that of the driving gear.

(b) be opposite to the driving gear.

(c) depend upon the number of teeth on the driving gear.

(d) depend upon the total number of teeth on all gears of the train.

12 Consider the following statements in case of reverted gear train:

1. The direction of rotation of the first and the last gear is the same.

2. The direction of rotation of the first and the last gear is opposite.

3. The first and the last gears are on the same shaft.

4. The first and the last gears are on separate but coaxial shafts.

Which of these statements is/are correct ?

(a) 1 and 3 (b) 2 and 3 (c) 2 and 4 (d) 4 alone

13 The dynamic load on a gear is due to

1. inaccuracies of tooth spacing.

2. irregularities in tooth profile.

3. deflection of the teeth under load

4. type of service(i.e. intermittent, one shift per day, continous per day.)

Which of the above statements are correct ?

(a) 1, 2 and 3 (b) 2, 3 and 4

(c) 1, 3 and 4 (d) 1, 2 and 4

14 Consider the following statements:

A 20 stub tooth system is generally preferred in spur gears as it results in.

1. stronger teeth.

2. lesser number of teeth on the pinion.

3. It is restrained to expand or contract freely.

4. reduction of interference.

Which of the above statements are correct ?

(a) 1,2 and 4 (b) 3 and 4 (c) 1 and 3 (d) 1, 2, 3 and 4

15 An epicylic gear train has 3 shaftsA, B and C.Ais an input shaft running at 100 rpm clockwise. B is an

output shaft running at 250 rpm clockwise. torque onAis 50 kNm (clockwise).C is a fixed shaft. The

torque to fix C.

(a) is 20 kNm anticlockwise (b) is 30 kNm anticlockwise.

(c) 30 kNm clockwise. (d) cannot be determined as the data is insufficient

16 Consider the following modifications regarding avoiding the interference between gears:

1. The centre distance between meshing gears be increased

2.Addendum of the gear be modified.

3. Teeth should be undercut slightly at the root.

4. Pressure angle should be increased.

5. Circular pitch be increased.

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MECHANICAL ENGINEERING

Which of these are effective in avoiding interference.?

(a) 1, 2 and 3

(b) 2, 3, 4 and 5

(c) 1, 4 and 5

(d) 3, 4 and 5

17 In a reverted gear train, two gears P and Q are meshing, Q-R is a compound gear, and R and S are

meshing. The modules of P and R are 4 mm and 5 mm respectively. The numbers of teeth in P,Q and R

are 20,40 and 25 respectively. The number of teeth in S is.

(a) 23 (b) 35 (c) 50 (d) 53

18 When two spur gears having involute profiles on their teeth engage, the line of action is tangential to the.

(a) Pitch circles

(b) Dedendum circles

(c)Addendum circles

(d) Base circles

19 If the annular wheel of an epicyclic gear train has 100 teeth and the planet wheel has 20 teeth, the

number of teeth on the sun wheel is.

(a) 80 (b) 60

(c) 40 (d) 20

20 Match list - I (gears) list - II (configuration) and select the correct answer:

List - I List - II

A. Spur - 1. Connecting two nonparallel or intersecting but coplanar shafts.

B. Bevel - 2. Connecting two parallel and coplanar shafts with teeth parallel to the axis of the gear wheel.

C. Helical - 3. Connecting two parallel and coplanar shafts with teeth inclined to the axis of the gear wheel.

D. Mitre - 4. Connecting two shafts whose axes are mutually perpendicular to each other.

Codes :-

ABCD

(a) 2 4 3 1

(b) 3 1 2 4

(c) 2 1 3 4

(d) 3 4 2 1

21 The gears employed for connecting two non-intersecting and nonparallel, i.e, non-coplanar shafts are.
(a) Bevel gears
(b) Spiral gears
(c) Helical gears
(d) Mitre gears

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THEORY OF MACHINE

22 Two shaftsAand B in the same straight line are geared together through an intermediate parallel shaft.

The parameters relating to the gears and pinions are given in the table:

Item Speed Teeth PCD Module

Driving WheelA NA TA DA m

Driven Wheel B NB TB DB m

Driven wheel C on NC TC DC m

the intermediate shaft

Driving wheel D On the ND TD DD m

Intermediate shaft, in mesh

with B

Which of the following relations is not valid for kinematic design considerations ?

(a) NA = TC x TB (b) NA = TC x TB

NB TA TD NB TA TD

(c) DA + DC = DB + DD. (d) TA + TC = TB + TD.

23 Two points,Aand B located along the radius of a wheel, as shown in the fig above, have velocities of
80 and 140 m/s, respectively. The distance between pointsAand B is 300 mm. The radius of wheel is.
2

2

AB
1

(a) 400 mm (b) 500 mm
(c) 600 mm (d) 700 mm

24 Consider the following statements regarding improvement of efficiency of worm gear drive.
1. Efficiency can be improved by increasing the spiral angle of worm thread to 45o or more.

2. Efficiency can be improved by adopting proper lubrication.

3. Efficiency can be improved by adopting worm diameter as small as practicable to reduce sliding

between worm-threads and wheel teeth.

4. Efficiency can be improved by adopting convex too profile both for worm and wheel.

Which of the statements given above are correct ?

(a) 1, 2 and 3 (b) 1, 2 and 4

(c) 2, 3 and 4 (d) 1, 3 and 4

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MECHANICAL ENGINEERING

25 Which type of gears are used for shaft axes having an offset?

(a) Mitre gears (b) Spiral bevel gears

(c) Hypoid gears (d) Zerol gears

26 Spiral gears are used to connect:

(a) Two parallel shafts.

(b) Two intersecting shafts.

(c) Two nonparallel and non intersecting shaft

(d) None of the above.

27 Consider the following statements pertaining to the basic Lewis equation for the strength design of spur

gear teeth:

1. Single pair of teeth participates in power transmission at any instant

2. The tooth is considered as a cantilever beam of uniform strength.

3. Loading on the teeth is static in nature.

4. Lewis equation takes into account the inaccuracies of the tooth profile.

5. Meshing teeth come in contract suddenly.

Which of the statements given above are correct?

(a) 1, 3, 4 and 5 (b) 1, 2, 3 and 4 (c) 1, 2 and 3 (d) 2, 4 and 5

28 Match list - I (Type of Gear/Gear Train) with List - II

(Different Usage and drive) and select the correct answer using the code given below the lists:

List - I List - II

A. Epicyclic gear train - 1. Reduces and thrust

B. Bevel Gear - 2. Low gear ratio

C. Worm and worm gear - 3. Drives nonparallel non-intersecting shafts.

D. Herringbone Gear - 4. High gear ratio

Codes :

ABCD

(a) 5 4 3 1

(b) 2 3 4 5

(c) 5 3 4 1

(d) 2 4 3 5

29 Consider the following statements in respect of worm gears :

1. They are used for very high speed reductions.

2. The velocity ratio does not depend on the helix angle of the worm.

3. The axes of worm and gear are generally perpendicular and non-intersecting.

Which of the statements given above are correct?

(a) 1 and 2 (b) 1 and 3

(c) 2 and 3 (d) 1, 2 and 3

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THEORY OF MACHINE

30 Match list - I (Type of Gears) with List - II (Characteristics) and select the correct answer using the

code given below the lists:

List - I List - II

A. Helical gearing - 1. Zero axial thrust

B. Herringbone gearing - 2. Non-interchangeable

C. Worm gearing - 3. Skew shafts

D. Hypoid gearing - 4. Parallel shafts

Codes:

ABCD

(a) 4 1 3 2

(b) 3 2 4 1

(c) 4 2 3 1

(d) 3 1 4 2

31 Consider the following statements:

1. Astub tooth has a working depth larger than of a full depth tooth.

2. The path of contact for involute gears is an arc of a circle.

Which of the statements given above is / are correct ?

(a) 1 only (b) 2 only

(c) Both 1 and 2 (d) Neither 1 nor 2

32 What is the value of pressure angle generally used for involute gears ?

(a) 35o (b) 30o (c) 25o (d) 20o.

33 Which one of the following is the correct statement ?

In meshing gears with involute gear teeth, the contact begins at the intersection of the.

(a) Line of action and the addendum circle of the driven gear.

(b) Line of action and the pitch circle of the driven gear.

(c) Dedendum circle of the driver gear and the addendum circle of the driven gear.

(d)Addendum circle of the driver gear and the pitch circle of the driven gear.

34 Interference between the teeth of two meshing involute gears can be reduced or eliminated by.

1. Increasing the addendum of the gear teeth and corresponding reducing the addendum of the pinion.

2. Reducing the pressure angle of the teeth of the meshing gears .

3. Increasing the centre distance.

Which of the statements given above is/are correct ?

(a) 1 and 2 (b) 2 and 3

(c) 1 only (d) 3 only

35 Gearing contact is which one of the following ?

(a) Sliding contact

(b) Sliding contact, only rolling a pitch point.

(c) Rolling contact.

(d) Rolling and sliding at each point of contact.

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MECHANICAL ENGINEERING

36 Interference between an involute gear and a pinion can be

reduced by which of the following ?

1. Increasing the pressure angle of the teeth in the pair, the

number of teeth remaining the same.

2. Decreasing the addendum of the gear teeth and increasing the same for the pinion teeth by the

corresponding amount.

Select the correct answer using the code given below:

(a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2

37 Common contact ratio of a pair of spur pinion and gear is.

(a) less than 1.0 (b) equal to 1 (c) between 2 and 3 (d) greater than 3

38 Which one of the following is correct ?

When two teeth profiles of gears are conjugate, the sliding velocity between them

(a) is always zero, all through the path of contact.

(b) is zero, at certain points along the path of contact.

(c) is never zero anywhere on the path of contact.

(d) can be made by proper selection of profiles.

39 For a speed ratio of 100 smallest gear box is obtained by using which of the following ?

(a) A pair of spur gears

(b) A pair of bevel and a pair of spur gears in compound gear train.

(c)A pair of helical and a pair of spur gears in compound gear train.

(d) Apair of helical and a pair of worm gears in compound gear train.

40 An external gear with 60 teeth meshes with a pinion of 20 teeth, module being 6 mm. What is the centre

distance in mm ?

(a) 120 (b) 180 (c) 240 (d) 300

41 A gear having 100 teeth is fixed and another gear having 25 teeth revolves around it, centre lines of both

the gears being jointed by an arm. How many revolutions will be made by the gear of 25 teeth for one

revolution of arm?

(a) 3 (b) 4 (c) 5 (d) 6

Out-

42 T3=...........1......0 ................. put

...........s......haft
T4

................. ................. ................. T 2

T1= 35
60
m m Input

shaft

In the fig shown above, if the speed of the input shaft of the spur gear train is 2400 rpm and the speed

of the output shaft is 100 rpm, what is the module of the gear 4 ?

(a) 1.2 (b) 1.4 (c) 2 (d) 2.5

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THEORY OF MACHINE

Class Room Objectives
1 - b, 2 - c, 3 - b, 4 - a, 5 - d, 6 - a, 7 - a, 8 - b, 9 - d, 10 - b, 11 - a, 12 - b, 13 - c, 14 - c, 15 - c,
16 - a, 17 - d, 18 - a, 19 - b.

Pactice Objectives
1 - b , 2 - d, 3 - a, 4 - c, 5 - c, 6 - d , 7 - a, 8 - d, 9 - d, 10 - d, 11 - c, 12 - d, 13 - a, 14 - a ,15 - b,16
- b , 17 - a, 18 - d, 19 - b, 20 - c , 21 - b, 22 - b, 23 - d, 24 - d, 25 - c, 26 - c , 27 - c, 28 - a, 29 - d,
30 - a,31 - a, 32 - d, 33 - a, 34 - d, 35 - b,36 - c, 37 - c, 38 - a , 39 - d, 40 - c, 41 - c, 42 - b

“The height of your accomplishments will equal
the depth of your convictions”

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MECHANICAL ENGINEERING

3 FLYWHEEL

Class Room Objectives :

1. For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc,

is required for keeping the fluctuation of speed within 2% about the average speed. The fluctuation

of kinetic energy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its

diameter is not to exceed 1m ? (GATE-03)

a) 40 kg b) 51 kg

c) 62 kg d) 73 kg

2. If C1 is the coefficient of speed fluctuation of a flywheel then the ratio of max/min will be

(GATE-06)

1 - 2C b) 2 - C1

a) 1 2+C
1
1 + 2C1
1 + 2C d) 2 + C1

c) 1 2-C
1
1 - 2C1

3. The speed of an engine varies from 210 rad/s to 190 rad/s. During cycle the change in kinetic energy

is found to be 400 Nm. The intertia of the flywheel in kgm2 is (GATE-07)

a) 0.10 b) 0.20

c) 0.30 d) 0.40

4. In terms of theoretical stress concentration factor (Kt) and fatigue stress concentration factor (Kt),

the notch sensitivity ‘q’ is expressed as (GATE-04)

(k - 1) (k - 1)

a) t b) t

(kt - 1) (kt +1)

c) (kt - 1) d) (kt + 1)

(kt - 1) (k - 1)
t

5. The S-N curve for steel becomes asymptotic nearly at (GATE-04)

a) 103 cycles b) 104 cycles c) 106 cycles d) 109 cycles

6. A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000

cycles is 490 MPa. If the corrected endurance strength is 70 MPa, estimated shaft life will be

(GATE-06)

a) 1071 cycles b) 15000 cycles

c) 281914 cycles d) 928643 cycles

7. A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal

pressure varying from 4 to 8 MPa. Assume that the yield, ultimate, and endurance strength of

material are 600, 800 and 400 MPa respectively. The factor of safety as per Goodman’s relation is

(GATE-07)

a) 2.0 b) 1.6 c) 1.4 d) 1.2

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THEORY OF MACHINE

8. The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a

compressive force of 10 kN due to the internal pressure. The end conditions for the rod may be

assumed as guided at the piston end and hinged at the other end. The piston rod is (GATE-07)

a) 0.68 b) 2.75 c) 5.62 d) 11.0

9. A forged steel link with uniform diameter of 30 mm at the centre is subjected to an axial force that

varies from 40 kN in compression to 160 kN in tension. The tensile (Su), yield (Sy) and corrected

endurance (Se) strengths of the steel material are 600 MPa, 420 MPa and 240 MPa respectively.

The factor of safety against fatigue endurance as per Soderberg’s crtiterion is (GATE-09)

a) 1.26 b) 1.37 c) 1.45 d) 2.00

Practice Objectives
1 In a 4 - stroke I.C engine, the turning moment during the compression stroke is

(a) positive throughout
(b) negative throughout
(c) positive during major portion of the stroke
(d) negative during major portion of the stroke.

2 With reference to the engine mechanism shown in the given fig, match list - I with list - II and select

the correct answer.

FC
Fw

G FD

W O

FR
FQ

List - I List - II

A. FQ - 1. Inertia force of reciprocating mass.

B. FR - 2. Inertia force of connecting rod.

C.FW - 3. Crank effort

D. FC - 4. Piston side thrust.

3 In the case of a flywheel, the maximum fluctuation of energy is the.

(a) sum of maximum and minimum energies.

(b) difference between the maximum and minimum energies.

(c) ratio of the maximum and minimum energy.

(d) ratio of the minimum and maximum energy.

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MECHANICAL ENGINEERING

4 Consider the following parameters:

1. Limit of peripheral speed.

2. Limit of centrifugal stress

3. Coefficient of fluctuation of speed.

4. Weight of the rim.

5 If the rotating mass of a rim type flywheel is distributed on another rim type fly wheel whose mean

radius is half the mean radius of the former, then energy stored on the latter at the same speed will

be.

(a) four times the first one (b) same as the first one

(c) one - fourth of the first one (d) two times the first one

6 The fluctuation of energy Ef , during a cycle for a flywheel is
(a) l (2max -2min ) (b) ½ lav(2max -2min )

(c) 1/ 2 lKes 2av (d) lKes 2av.

(where l = Mass moment of inertia of the flywheel

av = Average rotational speed
Kes= coefficient of fluctuation of speed )
7 For minimizing speed fluctuations of an engine as a prime mover . it must have.

(a) Only a flywheel fitted to the crankshaft.

(b)Agovernor provided in the system.

(c) Both a flywheel and a governor provided in the system

(d) Neither a flywheel nor a governor.

8 What is the value of the radius of gyration of disc type flywheel as compared to rim type flywheel for

the same diameter ?

(a) 2 times (b) 1 / 2 times

(c) 2 times (d) 1 / 2 times.


9

Torque


/2  
/2 

The crank of a slider - crank punching press has a mass moment of inertia of 1 kgm2. The above fig

shows the torque demand per revolution for a punching operation. If the speed of the crank is found

to drop from 30 rad/s to 20 rad/s during punching, hat is the maximum torque demand during the

punching operation ?

(a) 94.4 Nm (b) 104.7 Nm

(c) 477.2 Nm (d) 523.8 Nm

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THEORY OF MACHINE

10 In which one of the following is a flywheel generally employed ?

(a) Lathe (b) Electric motor

(c) Punching machine (d) Neither 1 nor 2

11 The turning moment diagram for a single cylinder double acting steam engine consists of +ve and

-ve loops above and below the average torque line. For the +ve loop, the ratio of the speeds of the

flywheel at the beginning and the end is which one of the following ?

(a) Less than unity (b) Equal to unity

(c) Greater than unity (d) Zero

12 A machine is coupled to a power source. The machine requires constant torquebut torque supplied

by the power source is (800 + 200 sin ) N-m. Mass moment of inertia of the flywheel is
400 kg-m2, what is the maximum angular acceleration of the flywheel and at what position does it

occur ?
(a) 0.5 rad/sec2 at = 90o. (b) 1.0 rad/sec2 at = 90o.
(c) 0.5 rad/sec2 at = 180o. (d) 2.0 rad/sec2 at = 90o.
13 In a flywheel, the safe stress is 25.2 MN/m2 and the density is 7 g/cm3. Then what is the maximum

peripheral velocity ?

(a) 30 m/s (b) 45 m/s (c) 60 m/s (d) 120 m/s

14 The given fig. shows the turning moment diagram of an engine. the mean speed of prime mover is 2

rad/s and the mass moment of inertia is 0.1 kg-m2 , then what is the coefficient of fluctuation of

energy ?

Torque in N-m 1200
1000
800

0 90 180 270 360
Crank angle in deg

(a) 1 % (b) 5 % (c) 7.5 % (d) 10 %

***********************

“If you think you can, you can.
And if you think you can’t you’re right”

CLASS ROOM OBJECTIVES
1 - b, 2 - d, 3 - a, 4 - b, 5 - c, 6 - c, 7 - b , 8 - c, 9 - a.
PRACTICE OBJECTIVES
1 - b , 2 - c, 3 - b, 4 - d, 5 - c, 6 - d , 7 - b, 8 - b, 9 - c, 10 - c, 11 - a,
12 - a, 13 - b, 14 - ,

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MECHANICAL ENGINEERING

4 VIBRATIONS

Class Room Objectives

1 A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion.As it passes

through its mean position, the bob has a speed of 5 m/s.The net force on the bob at the mean position

is. (ME=05)

(a) zero (b) 2.5 N

(c) 5 N (d) 25 N

2 There are four samples P,Q,R and S with natural frequencies 64, 96, 128 and 256 Hz, respectively.

They are mounted on test setups for conducting vibration experiments. If a loud pure note of frequency

144 Hz is produced by some instrument, which of the samples will show the most perceptible induced

vibration ? (ME=05)

(a) P (b) Q (c) R (d) S

3 A mass M, of 20 kg is attached to the free end of a steelcantilever beam of length 1000 mm having a

cross-section of 25 x 25 mm.Assume the mass of the cantilever to be neglible and Esteel = 200 GPa.

If the lateral vibration of this system is critically damped using a viscous damper, the damping constant

of the damper is. (ME=04)

(a) 1250 Ns/m M
(b) 625 Ns/m

(c) 312.50 Ns/m

(d) 156.25 Ns/m

4 A flexible rotor - shaft system comprises of a 10 kg rotor disc placed in the middle of a mass-less shaft

of diameter 30 mm and length 500 mm between bearings (shaft is being taken mass-less as the equiva

lent mass of the shaft is included in the rotor mass) mounted at the ends. the bearings are assumed to

simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is

2.1 x 1011 Pa. What is the critical speed or rotation of the shaft ? (ME=03)

(a) 60 Hz (b) 90 Hz

(c) 135 Hz (d) 180 Hz

Data for Q.5 & 6 are given below
A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring and
damper arrangement as shown in the fig where K = 2 kN/m, C = 500 Ns/m and the stiffness of the torsional
spring K is 1 kNm/rad. Ignore the hinge dimensions.

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THEORY OF MACHINE

CK

Bar
K

400mm

500mm

5 The un-damped natural frequency of oscillations of the bar about the hinge point is.

(a) 42.43 rad/s (b) 30 rad/s (c) 17.32 rad/s (d) 14.14 rad/s

6 The damping coefficient in the vibration equation is given by :

(a) 500 Nms/rad (b) 500 N/(m/s) (c) 80 Nms/rad (d) 80 N/(m/s)

7 Consider the arrangement shown in the fig. below where J is the combined polar mass moment of

inertia of the disc and the shafts. K1, K2, K3 are the torsional stiffness of the respective shafts.

The natural frequency of torsional oscillation of the disc is given by. (ME-03)

J

K1 K2 K3

Fixed end

Fixed end

(a)  K1+ K2 + K3 (b)  K1K2 + K2K3 + K3K1

J J(K1+ K2)

(c) J(K1+ K2) (d) K1K2 + K2K3 + K3K1
 J(K2+ K3)
 J (K1K2 + K2K3 + K3K1)

8 The assembly shown in the fig. is composed of two massless rods of length l with two particles, each of

mass m. the natural frequency of this assembly for small oscillations is. (ME-01)

(a) g / l 
(b) 2g / (l cos)
(c) g / (l cos) m
(d) (g cos) / l

m

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MECHANICAL ENGINEERING

9 A spring mass dashpot system is shown in the fig. The spring stiffness is k, mass is m, and the viscous

damping coefficient is c. the system is subjected to a force F cos t as shown . Write the equations of

motion which are needed to determine x. (No need to determine x. ) (ME-01)

x

kc

m F0cos

10 As shown in Fig. a mass of 100 kg is held between two springs. The natural frequency of vibration of

the system, in cycles/s is K = 5 kN/m. (ME-2000)

(a) 1/2 K
(b) 5/ K
(c) 10 / 
(d) 20 / 100 kg

K

11 The natural frequency of an undamped vibrating system is 100 rad/s.Adamper with a damping factor

of 0.8 is introduced into the system. The frequency of vibration of the damped system, in rad/s, is

(ME-2000)

(a) 60 (b) 75

(c) 80 (d) 100

12 A mass of 1 kg is suspended by means of 3 springs as shown in fig. The spring constants ‘K1’,‘K2’ and

‘K3’ are repecitively 1 kN/m, 3 kN/m and 2 kN/m. The natural frequency of the system is

approximately. (ME-96)

(a) 46.90 rad/s K1 K3
(b) 52.44 rad/s
(c) 60.55 rad/s K2
(d) 77.46 rad/s
M = 1 kg

13 In a single degree of freedom vibration system, the undamped natural frequency is ........to/than the
damped natural frequency. (greater / equal / less) (ME-95)

14 The deflection of a spring with 20 active turns under a load of 1000N is 10mm. The spring is made into

two pieces each of 10 active coils and placed in parallel under the same load. The deflection of this

system is. (ME-95)

(a) 20 mm (b) 10 mm

(c) 5 mm (d) 2.5 mm

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THEORY OF MACHINE

15 A mass ‘m’ attached toa light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg

the period increases by 1 sec. The value of ‘m’ is (ME - 94)

(a) 1 kg (b) 1.6 kg

(c) 2 kg (d) 2.4 kg

16 High damping reduces the transmissibility if the non dimensional frequency ratio ‘n’ ( = forcing
frequency, n= natural frequency ).
[ME = 92]

(a) is less than 2 (b) is greater 2

(c) is less than 1/2 (d) is greater than 1/2

17 A mass of 2.5 kg is hung from a string of stiffness 3 kN/m the vibration is controlled by a dashpot and

it is found that the amplitude of the vibration diminishes to one-fourth of its initial value in five complete

oscillations.Assuming linear damping. Find the damping coefficient of the dashpot.

18 The differential equation governing the vibrating system is.
y 

k

m x
c

(a) mx + cx + k (x - y) = 0
(b) m (x - y) + c (x - y) = kx = 0
(c) m x + c(x - y) + kx = 0
(d) m (x - y) + c (x - y) + k (x - y) = 0

19 A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. Machine has an
unbalanced rotating force of 350 N at speed of 3600 rpm. Assuming a damping factor of 0.15, the
value of transmissibilityratio is.
(a) 0.0531
(b) 0.9922
(c) 0.0162
(d) 0.0028
A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with
damping co-effi cient of 15 Ns/m.

20 The value of critical damping of the system is
(a) 0.223 Ns/m
(b) 17.88 Ns/m
(c) 71.4 Ns/m
(d) 223.6 Ns/m

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MECHANICAL ENGINEERING

21 The value of logarithmic decrement is

(a) 1.35 (b) 1.32

(c) 0.68 (d) 0.68

22 For an under damped harmonic oscillator, resonance.

A. occurs when excitation frequency is greater than undamped natural frequency.

B. occurs when excitation frequency is less than undamped natural frequency.

C. occurs when excitation frequency is equal to undamped natural frequency.

D. never occurs [ME-07]

23 The natural frequency of the system shown below is [ME-07]

k/2
k

m

k/2 (b) k
m
(a) k
2m (d) 3k
m
(c) 2k
m

24 The equation of motion of a harmonic oscillator is given by [ME-07]

d2x + 2n dx + 2n x = 0,
d t2 dt

and the initial conditions at t = 0 are x (0) = X, dx / dt (0). The amlitude of x (t) after ‘n’ complete cycles

is

 (b) X e2nTT. 
(a) X e-2nTT. 1 - 2 1 - 2

1 - 2
(c) X e-2nTT.  (d) X

25 A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre and laterally supported

at one end by a spring of spring constant k = 300 N/m. The natural frequency n in rad/s is .

[ME-08]

(a) 10 (b) 20 (c) 30 (d) 40

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THEORY OF MACHINE

26 The natural frequency of the spring mass system shown in fig is closest to [ME-08]

(a) 8 Hz m = 1.4 kg
(b) 10 Hz
(c) 12 Hz k1 = 4000 N/m k2 = 1600 N/m
(d) 14 Hz

Previous IES Questions for Practice

1 The equation of free vibrations as a system is .. 1995 = 0. Its natural frequency is .
+ 362x
X

(a) 46 Hz (b) 3 Hz

(c) 3 Hz (d) 6 Hz

2 Which of the following methods can be used to determine the damping of machine element ?

1 Logarithmic method 2 Bandwidth method

3 Rayleigh method 4 Hozer method

Select the correct using the codes given below:

(a) 1 and 3 (b) 1 and 2

(c) 3 and 4 (d) 1, 3 and 4

3 If /n = 2, where  is the frequencyof excitation and n is the natural frequencyof vibrations, then

the trans-missibilityof vibrations will be:

(a) 0.5 (b) 1.0

(c) 1.5 (d) 2.0

4 A slender shaft supported on two bearing at its ends carries a disc with a eccentricity ‘e’ from the axis

of rotation. The critical speed of the shaft is N. If the disc is replaced by a second one of same weight

but mounted with an eccentricity 2e, critical speed of the shaft in the second case is.

(a) 1/2 N (b) 1 / 2 N

(c) N (d) 2 N

1996

5 When the mass of a criticallydamped single degree of freedom system is deflected from its equilibrium

position and released, it will.

(a) return to equilibrium position without oscillation

(b) oscillate with increasing time period.

(c) oscillate with decreasing amplitude

(d) oscillated with constant amplitude.

6 The equation of motion for a single degree of freedom system with viscous damping is

4X + 9X + 16X = 0 the damping ratio of the system is.

(a) 9 / 128 (b) 9 / 16

(c) 9 / 82 (d) 9 / 8

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MECHANICAL ENGINEERING

7 If two identical helical spring are connected in parallel and to these two, another identical spring is
connected in series and the system in loaded bya weight W, as shownin the figure, then the resulting
deflection will be given by ( = deflection, S = stiffness, W = load)

ss

s

(a) = 3W / 2S W
(c) = 2W / 3S
(b) = W / 2S

(d) = W / 3S

8 Two heavy rotating masses are connected by shafts of length l1,l2, and l3 and the corresponding
diameters are d1,d2, and d3. This system is reduced toa torsionally equivalent system having uniform
diameter d1 of the shaft. The equivalent length of the shaft is equal to.

(a) l1+ l2 + l3 (b) l1+ l2 + l3 / 3



(c) l1+ l2 d1 + l3 d1

d2 d3

(d) l1+ l2 
d1 d1

d2 + l3 d3

1999

9 Two identical spring labelelled as (1) and (2) and arranged in series and subjected to force F as shown
in the given figure.

12

F

Assume that each spring constant is K. The strain energy stored in spring (1) is

(a) F2/2K (b) F2/4K

(c) F2/8K (d) F2/16K

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THEORY OF MACHINE

2002

10 A shaft of 50 mm diameter and 1 m length carries a discwhich has mass eccentricity equal to 190

microns. The displacement of the shaft at a speed which is 90% of critical speed in microns is.

(a) 810 (b) 900

(c) 800 (d) 820

2007

11 Which one of the following causes whirling of shafts?

(a) Non - homogeneity of shaft material (b) Misalignment of bearings

(c) Fluctuation of speed (d) Internal damping

12 A uniform bar, fixed at one end carries a heavy concen-trated mass at the other end. The system is

executing longitudinal vibrations. The inertia of the bar may be taken into account by which one of the

following portions of the mass of the bar at the free end ?

(a) 5 / 384 (b) 1 / 48

(c) 33 / 140 (d) 1 / 3

13 A motion is aperiodic at what value of the damping

factor ?

(a) 1.0 or above (b) 0.5

(c) 0.3 (d) 0.866

14 m

k

r

A rolling disc of radius ‘r’and mass ‘m’is connected to one end of a linear spring of stiffness ‘k’ , as
shown in the above figure. The natural frequency of oscillation is given bywhich one of the following ?

(a)  = 2k (b)  =  k
m
 3m

(c)  = k 2k

 2m (d)  = m

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MECHANICAL ENGINEERING

2008

15 Consider the following statements:

1. One way of improving vibration isolation is to decrease the mass of the vibrating object.

2. For effective isolation, the natural frequency of the

system should be far less than the exciting frequency.

Which of the statements given above is/ are correct ?

(a) 1 only (b) 2 only

(c) Both 1 and 2 (d) Neither 1 nor 2

2009
16 A mass M vibrates on a frictionless platform between two sets of springs having individual spring

constant as shown in the figure below. What is the combined spring constant of the system ?

K1 K2
K1 M K2

Smooth

(a) K1 + K2 (b) 2 (K1 + K2)

(c) K1K2 (d) 2 (K1K2)
K1 + K2 K1 + K2

17 A reciprocating engine, running at 80 rad/s. is supported on springs. The static deflection of the spring
is 1 mm. Take g = 10 m/s2. When the engine runs, what will be the frequency of vibrations of the

system ?

(a) 80 rad/s (b) 90 rad/s

(c) 100 rad/s (d) 160 rad/s

18 The above figure shows two rotors connected by an elastic shaft undergoing torsional vibration. The

rotor 1 has a mass of 2 kg and a diameter of 60 cm, while the rotor 2 has a mass of 1 kg and a

diameter of 20 cm. What is the distance l at which the node of vibration of torsional vibration occurs ?

38cm

(a) 36 cm l
(c) 22 cm
2
1

(b) 30 cm
(d) 18 cm

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THEORY OF MACHINE

19 The static deflection of a shaft under a flywheel is 4 mm. Take g = 10 m/s2. what is the critical speed in

rad/s ?

(a) 50 (b) 20

(c) 10 (d) 5

20 Given below are the locations of the poles of a second - order closed -
Additional objectives for practice

1 The danger of breakage and vibration is maximum

(a) below critical speed

(b) near critical speed

(c) above critical speed

(d) none

2 Match list - I with list - II and select the correct answer using the codes give below the lists:

List - I List - II

Forces Mathematical expression

A. Inertia force - 1. C (dy / dt)
B. Spring force - 2. M (d2y / dt2)
C. Damping force - 3. M3 R

D. Centrifugal force - 4. Ky

Codes:

ABCD

(a) 1 3 2 4

(b) 2 4 1 3

(c) 2 1 4 3

(d) 1 2 3 4

3 With symbols having the usual meanings, the single

degree of freedom system, m x + c X + kx = F sin t represents.

(a) free vibration with damping

(b) free vibration without damping

(c) forced vibration with damping

(d) forced vibration without damping

4 A simple spring - mass vibrating system has a natural

frequencyof ‘N’. If the spring stiffness is halved and the mass is doubled, then the natural frequency will

become.

(a) N/2 (b) 2 N

(c) 4 N (d) 8 N

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MECHANICAL ENGINEERING

5 For the single degree of freedom system shown in the fig the mass M rolls along an incline of . The
natural frequency of the system will.

K X
M

(a) increase as  increases
(b) decrease as  increases
(c) be independent of 
(d) increase initially as increase and then decrease with further increase in .

6 Rotating shafts tend to vibrate violently at whirling speeds because.

(a) the shafts are rotating at very high speeds.

(b) bearing center line coincides with the axis

(c) the system is unbalanced

(d) resonance is caused due to the heavy weight of the rotor.

7 Critical speed of a shaft with a disc supported in between, is equal to the natural frequency of the

system in

(a) transverse vibrations

(b) torsional vibrations

(c) longitudinal vibrations

(d) longitudinal vibrations provided the shaft is vertical.

8 A mass of 1 kg is attached to the end of a spring with astiffness 0.7 N/mm. The critical damping co-

efficient of this system is.

(a) 1.40 (b) 18.522 Ns/m

(c) 52.92 (d) 529.20 Ns/m

9 Which of the following methods can used to determine the damping of a machine element?

1. Logarithmic method 2. Band - widthmethod

3. Rayleigh method 4. Holzer method

Select the correct answer using the codes given below:

(a) 1 and 3 (b) 1 and 2

(c) 3 and 4 (d) 1,3 and 4

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THEORY OF MACHINE

10 If (/n) = 2 where ‘’ is the frequency of excitation and ‘n’ is the natural frequency of vibrations,

then the transmissibilityof vibrations will be.

(a) 0.5 (b) 1.0

(c) 1.5 (d) 2.0

11 For the spring mass system shown in the fig- 1, the frequency of vibration is N. What will be the
frequency when one more similar spring is added in series as shown in fig-2 ?

1. 2.
k
(a) N/2 k
(b) N/2 m x
(c) 2 / N I1 k
(d) 2 N
m x

12 When the mass of a criticallydamped single degree of freedom system is deflected from its equilibrium
position and released, it will.
(a) return to equilibrium position without oscillation
(b) oscillate with increasing time period
(c) oscillated with decreasing amplitude
(d) oscillate with constant amplitude

13 The equation of motion for a single degree of freedom system with viscous damping is

4x + 9x + 16x = 0

(a) (9 / 128) (b) (9 / 16)

(c) (9 / 82) (d) (9 / 8)

14 For the spring - mass system shown in the given fig, the frequency of oscillations of the block along the
axis of the springs is.

k1 m k2

(a) 1/2(k1-k2/m)

(b) 1/2k1k2 / (k1+ k2)m
(c) 1/2(k1 + k2/m)
(d) 1/2m/(k1+ k2)

15 The critical speed of a rotating shaft depends upon

(a) mass (b) stiffness

(c) mass & stiffness (d) mass, stiffness & eccentricity

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MECHANICAL ENGINEERING

16 If air resistance is neglected, while it is executing small oscillations the acceleration of the bob of a
simple pendulum at the midpoint of its swing will be.
(a) zero
(b) a minimum but not equal to zero
(c) a maximum
(d) not determinable unless the length of the pendulum and the mass of the bob are known.

17 A damped free vibration is expressed by the general

equation.
x = Xe-nt sin (1 - 2nt + ) which is shown
graphically below:

The envelopeAhas the equation:

X A

Xsin  nt
O

(a) X e (b) X sin (1 - 2))nt
(c ) e- nt (d) X e-nt

18 What is the equivalent stiffness (i.e. spring constant) of the system in the given fig. ?

(a) 24 N/mm (b) 16 N/mm

(c) 4 N/mm (d) 5.3 N/mm

19 The given figure depicts a vector diagram of forces and displacements in the case of Forced Damped

Vibration. If factorArepresents the forcing function P = Po sin t, Vector B the displacement y = Ysin
t, and the angle between them, then the vectors C and D represent respectively.

 B

A  C

O

D

(a) the force of inertia and the force of damping
(b) the elastic force and the damping force
(c) the damping force and the inertia force
(d) the damping force and the elastic force

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