TOM Objective

THEORY OF MACHINE

THEORY OF MACHINES (Objective)

CONTENTS

Unit Chapters Page No.
1 Mechanisms, Velocity & Acceleration 2 - 26
2 Gears 27- 43
3 Flywheel 44 - 49
4 Vibration 50 - 76
5 Governors 77 - 85

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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 areω = 8 rad/s and α= 0,
respectively, and the driving torque (τ) is zero. The link O2Ais balanced so that its center of mass falls at O2

B
260

100
A

ω

α 60mm 160mm

τ 90o 90o

O2 O4

240mm

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. Scotch Yoke 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 its link lengths

(c) fixing its different 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 ω. 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) ω ( rB- rA) and direction opposite to the direction of motion of point B
(C) ω ( rB- rA) and direction same as the direction of motion of point B
(D) ω ( 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) ω ( rB2- rA2) and direction same as the direction of motion of point B
(C) ω2 ( rB- rA) and direction opposite to the direction of motion of point B
(D) ω2 ( 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) Scotch Yoke 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 feasibility of 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 V 0. 25 m C
(d) 0.2 m/s
B D

B VC
A θ=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. Mobility of 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
(d) 1 / √2 < O2P=O2Q4 = a

O2 O4

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

(a) 250 R11223344556677
(b) 250√ 3 Q
(c) 500
(d) 500 √ 3 ω = 2 rad/s

S

500 mm <> 11111111111111O22222222222222
P

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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 velocity at 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) ∞

31. A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick

return mechanism is 2 : 1. If the radius of the crank O P is 125 mm, then the distance ‘d’
1

(in mm) between the crank centre to lever pivot centre point should be (GATE-ME-09)

a) 144.3

b) 216.5

c) 240.0

d) 250.0

32. Mobility of a statically indeterminate structure is (GATE-ME-10)
a) < - 1
b) 0
c) 1
d) > 2

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THEORY OF MACHINE

33. There are two points P and Q on a planar rigid body. The relative velocity between the two

points (GATE-ME-10)

a) should always be along PQ

b) can be oriented along any direction

c) should always be perpendicular to PQ

d) should be along QP when the body undergoes pure translation

34. Which of the following statements is INCORRECT (GATE-ME-10)

a) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the

shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.

b) Inversion of a mechanism are created by fixing different links one at a time

c) Geneva mechanism is an intermittent motion device

d) Gruebler’s criterion assumes mobility of a planner mechanism to be one.

35. A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The

mobility of the mechanism is

a) -1

b) 0

c) 1

d) 2

36. A slide disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and

α(rα )2 + (rω )2 angular acceleration . The magnitude of the acceleration of the point of contact on the disc
is (GATE-ME-12)

a) zero b)

c) d) rω2

37. In the mechanism given below , if the angular velocity of the eccentric circular

disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the

figure is (GATE-ME-12)

Note : All dimensions are in mm

a) 0.05

b) 0.1

c) 5.0

d ) 10.0

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MECHANICAL ENGINEERING

38. A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction

and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to

the rod, as shown in the figure below. IF OA = 1 m, the magnitude of the absolute acceleration

of the block at location A in m/s2 is (GATE-ME-13)

a) 3

b) 4

c) 5

d) 6

39. A planner closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m

and SP = 2.7 m with all revolute joints. The link to the fixed to obtain a double rocker (rocker-

rocket) mechanism is (GATE-ME-13)

a) PQ b) QR c) RS d) SP

40. A circular object of radius r rolls without V slipping on a horizontal level floor with the center

having velocity V. The velocity at the point of contact between the object and the floor is

(GATE-ME-14)

a) zero

b) V in the direction of motion

c) V opposite to the direction of motion

d) V vertically upward from the floor

41. A rigid link PQ is 2 m long and oriented at 200 to the horizontal as shown in the figure. The

magnitude and direction of velocity V , and the direction of velocity V are given. The magnitude
QP

of V (in m/s) at this instant is (GATE-ME-14)
P

a) 2.14

b) 1.89

c) 1.21

d) 0.96

42. A 4-bar mechanism with all revolute pairs has link lengths l = 20 mm, l = 40 mm, l = 50 mm
f in co

and l = 60 mm. suffixes ‘f ’, ‘in’, ‘co’ and ‘out’ denote the fixed link, the input link, the coupler

out

and output link respectively. Which of the following statements is true about the input and

output links? (GATE-ME-14)

a) Both links can execute full circular motion

b) Both links cannot execute full circular motion

c) Only the output link cannot execute full circular motion

d) Only the input link cannot execute full circular motion

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THEORY OF MACHINE

43. For the given statements :
I. Mating spur gear teeth is an example of higher pair
II. A revolute joint is an example of lower pair

Indicate the correct answer (GATE-ME-14)

a) Both I and II are false

b) I is true and II if false

c) I is false and II is true

d) Both I and II are true

44. A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of

point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is

_______ (GATE-15-Set-1)

ω
2
45. In the figure, link 2 rotates with constant angular velocity ω2 . A slider link 3 moves outwards
with a constant relative velocity VQ/P, where Q is a point on slider 3 and p is a point on link 2.
The magnitude and direction of Coriolis component of acceleration is given by

(GATE-15-Set 3)

a) 2 V ; direction of V , rotated by 900 in the direction of
Q/P Q/P

b) V ; direction of V , rotated by 900 in the direction of
Q/P Q/P

c) 2 VQ/P; direction of VQ/P, rotated by 900 Opposite to the direction of
d) V ; direction of V , rotated by 900 Opposite to the direction of

Q/P Q/P

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MECHANICAL ENGINEERING

46. A rigid link PQ is undergoing plane motion as shown in the figure (V and V are non-zero). V QP
PQ

is the relative velocity of points Q with respect to point P. (GATE-16-Set 3)

Which one of the following is TR?UE ?

a) V has components along and perpendicular PQ
QP

b) V has only one component directed from P to Q
QP

c) V has only one component directed from Q to P
QP

d) V has only one component perpendicular to PQ
QP

47. The number of degrees of freedom in a planner mechanism having a links and j simple hinge

joints is (GATE-16-SET-3)

a) 3 (n -3) – 2j b) 3 (n – 1) – 2j c) 3n – 2j d) 2j – 3n + 4

48. Match the approaches given below to perform stated kinematics /dynamics analysis of machine

(GATE-ME-09)

Analysis Approach

P. Continuous relative rotation 1. D’ Alembert’s principle

Q. Velocity and acceleration 2. Grubler’s criterion

R. Mobility 3. Grashoff’s law

S. Dynamic – static analysis 4. Kennedy’s theorem

. PQRS
a) 1 2 3 4
b) 3 4 2 1
c) 2 3 4 1
d) 4 2 1 3

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THEORY OF MACHINE

49. For the configuration shown, the angular velocity of link AB is 10 rad/s counterclockwise. The
magnitude of the relative sliding velocity (in ms-1) of slider B with respect to rigid link CD is
(GATE-ME-10)
a) 0

b) 0.86

c) 1.25

d) 2.50

50. For the four – bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The

length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular

velocity of link CD in rad/s is (GATE-ME-11)

3
a) 3 b)

2

c) 1 d)

51. A slider-crank mechanism with crank radius 60 mm and connecting rod 240 mm is shown in the

figure. The crank is rotating with a uniform angular speed of 10 rad/s , counter clockwise. For
2 the given configuration, the speed (in m/s) of the slider is ___________ . (GATE-ME-14)
3

52. An offset slider – crank mechanism is shown in the figure at an instant. Conventionally, the

Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is

______________ (GATE-ME-14)

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MECHANICAL ENGINEERING

53. In a certain slider crank mechanism, lengths of crank and connecting road are equal. If the

crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the

maximum acceleration of the slider (in m/s2) is ____________. (GATE-15-Set 2)

54. The number of degree of freedom of the linkages shown in the figure is (GATE-15-Set 3)

a) -3
b) 0
c) 1
d) 2
55. Figure shows a wheel rotating, about O , Two points A and B located along the radius of wheel

2

have speed s of 80 m/s and 140 m/s respectively. The distance between the points A and B is
300 mm. The diameter of the wheel (in mm) is ____________________ (GATE-15-Set 3)

56. The an off-set slider crank mechanism, shown in figure, the crank is rotated at a constant

speed of 150 rpm. The value of the angle θ shown in the figure is 200. What is the ratio of

forward to return stroke time ? Can this mechanism be used in an application involving quick

return ? (GATE-PI-15)

a) 3.33, No
b) 0.73, yes
c) 1.25, yes
d) 0.73, No

57. The rod AB, of length 1 m shown in the figure is connected to two slider to two slider at each

end through pins. The slider can slide along QP and QR. If the velocity V of the slider at A is 2
A

m/s, the velocity of the midpoint of the rod at this instant is __________ m/s. (GATE-16- Set 2)

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THEORY OF MACHINE

Practice Questions :

1 Scoth yoke mechanism is used to generate

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

2 Inversion of a mechanism is

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

(b) obtained by fixing different links in a kinematic chain

(c) turning it upside down

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

3 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.

4 Consider the following statements :

Coriolis component of acceleration depends on

1. Velocity of slider 2. angular velocity of 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

5 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

6 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

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MECHANICAL ENGINEERING

7 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

8 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.

9 The direction of Coriolis component of acceleration 2 V, of the slider Awith 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 Vω V ↓↓ ω
(b) 1 and 2 are wrong ↓↓2ωV
2ωV B2ωV B B 2ωVB
A AA A
↓↓
↓↓
(c) 1 and 3 are wrong ω V↓ ω V ↓
(d) 2 and 3 are wrong
O OO O

10 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

11 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) infinity alongAC

(d) infinity perpendicular to BD

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THEORY OF MACHINE

12 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

13 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
14 When a slider moves with a velocity ‘V’ on a link rotating at an angular speed of ω,the Corioli’s

component of acceleration is given by.
(a) √2 Vω.
(b) Vω.
(c) Vω/ 2
(d) 2 Vω

15 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

16 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

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MECHANICAL ENGINEERING

17 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

18 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 A will be.

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

19 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

20 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

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

(a) Structure © Copyright : Ascent Gate Academy 18
(b) mechanism with one degree of freedom
(c) mechanism with two degrees of freedom
(d) mecahnism with more than two degrees of freedom

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THEORY OF MACHINE

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

(a) straight line

(b) circle

(c) parbola

(d) ellipse

23 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

24 Consider the following statements:

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

2. A square 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

25 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.

26 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

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MECHANICAL ENGINEERING

27 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
Codes :
ABCD

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

28 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

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THEORY OF MACHINE

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) Both Aand R are individually true and R is the correct explanation of A.

(b) Both A and R are individually true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is 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.

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. A road 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.

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Codes : A MECHANICAL ENGINEERING
5
(a) 4 BCD
(b) 5 243
(c) 4 312
(d) 342
213

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.

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

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THEORY OF MACHINE

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.

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)

(a) 3 and 4 (3) (4) (d) 4 only.
© Copyright : Ascent Gate Academy 23
(b) 2 and 3 (c) 3 only

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MECHANICAL ENGINEERING

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

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

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THEORY OF MACHINE

17 (06)

B

A

Assertion (A): LinkAexperiences Coriolis acceleration relative to the fixed link.

Reason (R) : Slotted link A is rotating with angular velocity w and the Block slides in the slot of A.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A 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.

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. Mobility of linkages.

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

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MECHANICAL ENGINEERING

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.
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
One Mark Questions
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.
31-d, 32-a, 33-c, 34-a, 35-c, 36-d, 37-c, 38-c, 39-c, 40-a, 41-d, 42-a, 43-d, 44-20, 45-a, 46—d, 47-
b, 48-b, 49-d, 50-d, 51- 0.618, 52-1.125, 53-117.6, 54-c, 55=1400, 56-c, 57-a

Practice Questions
1-a, 2-b, 3-c, 4-a, 5-a, 6-d, 7-b, 8-c, 9-a, 10-d, 11-a, 12-a, 13-d, 14-d, 15-d, 16-c, 17-d, 18-b, 19-c,
20-a, 21-b, 22-d, 23-d, 24-d, 25-a, 26-b, 27-c, 28-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) 11111112222222111133333332222333344445555666677778888999900001111222233334444555566667777888899991111111000022222223333333

========= 1000 N

→ →RACK
→
111111111111111111112222222222222222222233333333333333333333 T = 80 T = 80 111111111111111111112222222222222222222233333333333333333333
=========
1122334455 11223344
-------

T = 20

MOTOR

11223344556677889900

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 ω1, ω2, ω and ω4,
3
respectively. The carrier rotates with angular velcity ω5.
(GATE-06)

Gear 2 `’ Gear 3
45T `’ 20T

111222333444555666777 1122334455
11223344556677 ------11--22--33--44--55--

Gear 1 Carrier 5
15T
Gear 4
40T

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

ω - ω ω - ω
1 5 4 5
a) = 6 b) = 6
ω - ω ω - ω
4 5 1 5

c) ω - ω 2 d) ω - ω 8
1 2 2 5
= - =
ω - ω 3 ω - ω 9
4 5 4 5

5. For ω = 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 (Z2 teeth) and pinion (Z3 = 15 teeth) to mesh with pinion (Z1 = 16 teeth) on the input shaft and gear (Z4
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

16. Match the type of gears with their most appropriate description (GATE-08)

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

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THEORY OF MACHINE

20. Tooth interference in an external involute spur gear pair can be reduce by (GATE-ME-10)

a) decreasing center distance between gear pair

b) decreasing module

c) decreasing pressure angle

d) increasing number of gear teeth

21. The following are the data for two crossed helical gears used for speed reduction

Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 300

Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.50

If the input speed is 1440 rpm. The output speed in rpm is (GATE-ME-12)

a) 1200

b) 900

c) 875

d) 720

22. Which one of the following is used to convert a rotational motion into a translation motion ?

(GATE-ME-14)

a) Bevel gears

b) Double helical gears

c) Worm gears

d) Rack and pinion gears

23. A gear train is made up of five spur gears shown in the figure. Gear 2 is driver and gear 6 is

driven member. N2, N3, , N4, N5and N6 respectively. The gear(s) which act(s) as idler (s) is/are
(GATE-15-Set -3)

a) only 3
b) only 4
c) only 5
d) both 3 and 5

24. The number of degrees of freedom of the planetary gear train shown in the figure is
(GATE-15-Set-2)

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

(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, 20-d, 21-b, 22-d, 23-c, 24-c

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MECHANICAL ENGINEERING

Two Marks Questions :

1. An epicyclic gear train is shown schematically in the 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 gear 5 is a 100 teeth internal gear. The gear 5 is fixed and the gear 2 is

rotating at 60 rpm CCW (CCW = counter-clockwise and CW = clockwise). The arm 4 attached to

the output shaft will rotate at (GATE-ME-09)

a) 10 rpm CCW

b) 10 rpm CW

c) 12 rpm CCW

d) 12 rpm CW

2. For the epicyclic gear arrangement shown in the figure, ω = 100 rad/s clockwise (CW) and
2

ω = 80 rad/s counter clockwise (CCW). The angular velocity (in rad/s) is (GATE-ME-10)
arm

a) 0

b) 70 CW

c) 140 CCW

d) 140 CW

3. A compound gear train with gears P, S, R & S has number of teeth 20, 40, 15 and 20 respectively.

Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of

the gear Q is twice that of the gear R. If the module of the gear R is 2 mm , center distance in

mm between gears P and S is (GATE-ME-13)

a) 40
b) 80
c) 120
d) 160

4.) Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with gear 3. Gear 3 and
Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4, The number of teeth on
Gear 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is.

(GATE-ME-14)

a) 300 rpm counter clockwise
b) 300 rpm clockwise
c) 4800 rpm counter clockwise
d) 4800 rpm clockwise

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THEORY OF MACHINE

5. It is desired to avoid interference in a pair of spur gears having a 200 pressure angle. With

increase in pinion to gear speed ratio, the minimum number of teeth on the pinion.

(GATE-ME-14)

a) increases

b) decreases

c) first increases and then decreases

d) remains unchanged

6. A pinion with radius r1 and inertia I1, is driving a gear with radius r2 and inertia I2. Torque ι is

1

applied on pinion. The following are free body diagrams of pinion and gear showing forces

(F1 and F2) of interaction. Which of the following relations hold true ? (GATE-15-Set 1)

a)
b)

c)
d)

7. In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The
number of teeth on gear 2, 3 and 4 are 60, 20 and 100, respectively. If gear 2 is fixed and gear
4 rotates with an angular velocity of 100 rpm in the counterclockwise direction, the angular
speed of arm 5 (in rpm) is
(GEAR-16-SET-1)

a) 166.7 counterclockwise
b) 166.7 clockwise
c) 62.5 counterclockwise
d) 62.5 clockwise

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MECHANICAL ENGINEERING

Five Marks Questions :

1. Below fig show a planetary gear train. Gears 2, 4 and 5 have 24, 40 and 144 teeth respectively.

Gear 5 is fixed. Gear 2 is rotating clockwise at 700 rpm. What will be the rpm of the arm and

gear 4 ? (GATE-ME-96)

2. A planetary gear train is shown in the figure. Internal gear (1) has 104 and is a held fixed on

planet gear (2) has 96 teeth. How much does the planet gear rotates for sixty revolutions of the

planet carrier (3) in clock wise direction ? AAGATE-ME-99)

3. Gear & Gear Trains © Copyright : Ascent Gate Academy 34
Two Marks Ans.
1-a, 2-c, 3-b, 4-a, 5-a, 6-b, 7-c
Five Marks Ans.
1-460 rpm (CW), 2-5 rpm in CCW

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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 A is 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 αa and αb respecitvely
are meshed to gather.Brotates at G times the speed of A. If the gearing efficiency of the two shafts in
η then in order to accelerate B, the torque which must be applied to A will be.

(a) 1aαa+ G2l bαb / η. (b) G2l bαa η.
(c) G2la αa η. (d) G2lb αb η.

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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 Product of teeth on the follower

(c) Product of teeth on the follower (d) Product of teeth on the drivers

9 Consider the following pairs of parts: 2. Belt and pulley
1. Pair of gear in mesh 4. Cam and follower
3. Cylinder and piston
Among these, the higher pairs are (b) 2 and 4
(a) 1 and 4 (d) 1, 2 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) Both Aand R are individually true and R is the correct explanation of A.
(b) Both A and R are individually true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is 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.
ω2

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. A stub 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) A pair 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-
put
42 T3=...........1......0 .................
...........s......haft
T4

................. ................. → ................. T 2

T1= → 35

60 mm → 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 ωmax/ωmin will be
(GATE-06)

a) 1 - 2C1

1 + 2C1

b) 2 - C1

2 + C1

c) 1 + 2C1

1 - 2C1
2+C

d) 1

2 - C1

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

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THEORY OF MACHINE

4. A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a fly
wheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in joules is
(GATE-ME-12)
a) 396
b) 700
c) 1580
d) 3160

5. Consider the slider crank mechanism with nonzero masses and inertia. A constant torque is
applied on the crank as shown in the figure. Which of the follwoing plots best resembles variation of
crank angle, versus time
(GATE-15-Set 1)

a) b)

c) d)

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MECHANICAL ENGINEERING

6. A flywheel connected to a punching machine has to supply energy of 400 Nm while runing at a mean

angular speed of 20 rad/s. If the total flucuation of speed is not to exceed +2%, the mass moment of

inertia of the flywheel in kg-m2 is (GATE-ME-13)

a) 25 b) 50 c) 100 d) 125

7. Consider a flywheel whose mass M is distributed almost equally between a heavy, ring-like rim of

radius R and a concentric disk-like feature of radus R/2. Other parts of the flywheel, such as spokes,

etc, have negligible mass. The best approximation for , if the moment of inertia of the fly wheel

about its axis of rotation is expressed as MR2, is ________________ (GATE-ME-14)

8. Maximum fluctuation of kinetic energy in an engine has been calculated to be 2600 J.Assuming that

the engine runs at an average speed of 200 rpm, the polar mass moment of inertia (in kg.m2) of a

flywheel to keep the speed flucuation within +0.5% of the average speed is __________

(GATE-ME-14)

9. Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figure.

The moment of intertia (in kg.m2) of the flywheel is _____________ (GATE-ME-14)

10. The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as

T = 10000+1000sin2 - 1200 cos2 , where is the crank angle as measured from inner dead

center position.Assuming the resisting torque to be constant, the power (in kW) developed by the

engine at 100 rpm is ____________ (GATE-15-Set 3)

11. An engine, connected with a flywheel, is designed operate at an average angular speed of 800 rpm.

During operation of the engine. the maximum change in kinetic energy in a cycle is found to be

6240 J. In order to keep the function of the angular speed within +1% of its average value, the

moment of inertia (in kg-m2) of the flywheel should be ___________ (GATE-PI-16)

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THEORY OF MACHINE

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.

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

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MECHANICAL ENGINEERING

6 The fluctuation of energy Ef , during a cycle for a flywheel is
(a) l (ω2max - ω2min ) (b) ½ lωav(ω2max - ω2min )

(c) 1/ 2 lKes ω2av (d) lKes ω2av.

(where l = Mass moment of inertia of the flywheel

ωav = 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 ? (b) 1 / √2 times
(a)√ 2 times

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

↓↓
9

Torque

1111111111111222222222222233333333333334444444444444555555555555566666666666667777777777777 ↓
3π /2 2π θ
π /2 π

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

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

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THEORY OF MACHINE

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

by the power source is (800 + 200 sinθ ) 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 atθ = 90o. (b) 1.0 rad/sec2 atθ = 90o.
(c) 0.5 rad/sec2 atθ = 180o. (d) 2.0 rad/sec2 atθ = 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 2π

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 %

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

CLASS ROOM OBJECTIVES
1 - b, 2 - d, 3 - a, 4-b, 5-d, 6-a, 7-0.5625, 8-592.73, 9-31.42, 10-104.32, 11-44.45

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 - ,

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

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MECHANICAL ENGINEERING

4 VIBRATIONS

Class Room Objectives

1 Asimple 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 Kθ is 1 kNm/rad. Ignore the hinge dimensions.

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