TOM Objective

THEORY OF MACHINE

CK

Bar
Kθ

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 αα
(b) √2g / (l cosα) m
(c) √g / (l cosα)
(d) √(g cosα) / l

m

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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) 1/2π K
(b) 5/π K
(c) 10 / π
(d) 20 /π 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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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 ‘ω/ωn’ ( ω = forcing
frequency, ωn= 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 transmissibility ratio 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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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 + 2ξωn dx + ω2n 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

ξ (b) X e2nTT. ξ
(a) X e-2nTT. √1 - ξ 2 √1 - ξ 2

√1 - ξ 2
(c) X e-2nTT. ξ (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 ωn in rad/s is .

[ME-08]

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

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THEORY OF MACHINE [ME-08]

26 The natural frequency of the spring mass system shown in fig is closest to

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

27. The rotro shaft of a large electric motor supported between short bearings at both the ends shows a

deflection of 1.8 mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and

supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is

(GATE-ME-09)

a) 350 b) 705 c) 2810 d) 4430

28. The natural frequny of a spring mass system on earth is . The natural frequency of this system on the

moon (gmoon = gearth 6) is c) 0.204 (GATE-ME-10)
a) b) 0.408 d) 0.167

29. If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long

slender rotating shaft, the first critical speed of the shaft in rpm is (GATE-ME-13)

30. Critical damping is the (GATE-ME-14)

a) largest amount of dampoing for which no oscillation occurs in free vibration
ωn2 b) smallest amount of dampoing for which no oscillation occurs in free vibration

c) largest amount of damping for which the motion is simple harmonic in free vibration

d) smallest amount of dampoing for which the motion is simple harmonic in free vibration

31. In vibration isolation, which one of the follwoing statements is NOT correct regarding Transmissibility

(T) ? (GATE-ME-14)

a) T is nearly unity at small excitation frequencies

b) T can be always reduced by using higher dampiong at any eitation frequency

c) T is unity at the frequency ratio of

d) T is infinity at resonane for undamped systems

32. Consider a single degree-of-freedom system with viscous damping excited by a hormonic force. At

resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

(GATE-ME-14)

a) 0 b) 45 c) 90 d) 135

33. A Point mass is executive simple hormonic motion with an amplitude of 10 mm and frequency of 4 Hz.

The maximum acceleration (m/s2) of the mass is __________ . (GATE-ME-14)

34. In a spring-mass system the mass is m and the spring constant is k. The critical damping cofficient of the

system is 0.1 kg/s. In another spring mass system, the mass is 2m, and the spring constant is 8k. The

critical damping coefficient (in kg/s) of the system is __________ . (GATE-15-Set-2)

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35. Which of the following statements are TRUE for damped vibrations ? (GATE-15-Set 3)

P. For a system having critical damping the value of damping ratio is unity and system does not undergo

a vibratory motion.

Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.

R. In case of damping due to dry friction between moving surface resisting force of constant magnitude

acts opposite to the relative motion

S. For the case of viscous damping drag force is directly proportional to the square of relative velocity.

a) P and Q only b) P and S only c) P, Q and R only d) Q and S only

36. A simple degree of freedom spring mass system with viscous damping has a spring constant of

10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio)

is 0.25, the amplitude of steady state oscillation at resonance is _____ mm. (GATE-16-Set 1)

37. The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm.

Assume the acceleration frequency of this spring-mass system (in rad/s) is _________.

(GATE-16-Set 3)

TWO MARKS QUESTIONS :

38. An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of
the front two spring have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m.

The engine speed (in rpm), at which resonance is likely to occur is (GATE-ME-09)

a) 6040 b) 3020 c) 1424 d) 955

39. Avehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m

and the damping constant of the damper is 400 Ns/m. If the mass is 50 k, then the damping factor ( )

and damped natural frequency (fn) respectively are (GATE-ME-09)

a) 0.47 and 1.19 Hz b) 0.471 and 7.48 Hz

c) 0.666 and 1.35 Hz d) 0.666 and 8.50 Hz

40. A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without
slipping on a horizontal surface. The natural frequency of vibration of the systemj is (GATE-ME-11)

a)

1 2K
b) 2π m

1 2K
c) 2π 3m

1 3K
d) 2π 2m

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41. A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the
figure. Under frictionless condition. the natural frequency of the system in Hz is close to
(GATE-ME-11)
a) 32
b) 23
c) 16
d) 1

42. A concentrated mass m is attached at the centre of a rod of length 2L. as shown in the figure. The rod
is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of
vibration neglecting the weights of the rod and spring the un damped natural frequency of the system is
(GATE-ME-12)

a) K
m

b)

c)

542KKK
2mmm d)

43. A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected

to an impulse force of magnitude 5 kN for 10-4 seconds. The amplitude in mm of the resulting free

vibration is (GATE-ME-13)

a) 0.5 b) 1.0 c) 5.0 d) 10.0

44. Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The

frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip is 100Hz. The flexural

rigidity (in N.m2) of the beam is ___________. (GATE-ME-14)

45. Arigid uniform rodAB of length L and mass m is hinged at C such thatAC = L/3. CB = 2L/3. EndsA

and B are supported by springs of spring constant k. The natural frequency of the system is given by

(GATE-ME-14)

a) b)

c) d)

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46. What is the natural frequency of the spring mass system shown below ? The contact between the block

and the inclined plane is frictionaless. The mass of the block is denoted by m and the spring constants

are denoted by k1 and k2 as shown below (GATE-ME-14)

a) b) K1 + K2
c) K1 − K2 4m

m d) K1 + K2
m

47. The damping ratio of a single degre of freedom spring-mass-damper system with mass of 1 kg, stiffness

100 N/m and viscous damping coefficient of 25 N.s/m is ________ (GATE-ME-14)

48. A mass-spring-dashpot system with mass m = 10 kg, spring constant K = 6250 N/m is excited by a

harmonic excitation of 10 cost (25t) N. At the steady state, the vibration amplitude of the mass is

40 mm. The damping coefficnet (C, in N.s/m) of the dashpot is _______ (GATE-ME-14)

49. A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping ratio 0.02.
The dynamic magnification factor at an excitation frequency of 1.5 rad/s is ________ .
(GATE-ME-14)

50. Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibrations of

the system shown in the figure is (GATE-15-Set 1)

a) 400 b)
1

c) d)

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51. A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the
eccentric mass on motor with respect to center of gravity (CG) of the mobile and the rest of the
dimension of the mobile phone are shown. The mobile is kept on a flat horizontal surface.

Given in addition that the eccentric mass = 2 grams, eccentricity = 2.19 mm, mass of the mobile = 90

grams, g = 9.81 m/s2. Uniform speed of the motor in RPM for which the mobile will get just lifted off the

ground at the end Q is approximately. (GATE-15-Set 1)

a) 3000 b) 3500 c) 4000 d) 4500

52. A precision instrument package (m = 1 kg) needs to be mounted on a surface vibrating at 60 Hz. It is

desired that only 5% of the base surface vibration amplitude be transmitted to the intrument. Assume

that the isolation is designed with its natural frequency significantly lesser than 60 Hz, so that the effect

of damping may be ignored. The stiffness (in N/m) of the required mounting pad is ____________.

(GATE-15-Set 1)

53. A single degree freedom spring mass subjected to a sinusoidal force of 10 N amplitude and frequency

ω along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and

n = 1 k undamped natural frequency is 10 . At steady state, the amplitude of vibration (in m) is approxi
2π
4m mately. (GATE-15-Set 2)

a) 0.05 b) 0.07 c) 0.70 d) 0.90

54. Figure shows a single degree of freedom system. The system consist of a mass less rigid bar OP hined

at O and a mass m at end P. The natural frequency of vibration of the system is (GATE-15-Set 3)

a)

b) fn = 1 k
2π 2m

c) fn = 1 k
2π m

d) fn = 1 2k
2π m

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55. The system shown in the figure consists of block A of masss 5 kg connected to a spring through a
massless rope passing over pulley B of radius r and mass 20 kg. The spring constant k is 1500 N/m. If
there is no slipping of the rope over the pulley, the natural frequency of the system is ____ rad/s.
(GATE-16-Set 2)

56. A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude.

3k
For an excitation frequency of , the ratio of the amplitude of steady state response to the static

m

deflection of the spring is _________ (GATE-16-Set 3)

57. A solid disc with radius a is connected to a spring at a point d above centre of the disc. The other end
of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass
of the disc is M and the spring constant is K. The polar moment of inertia for the disc about its centere
is

The natural frequency of this system is rad/s is given by (GATE-16-Set 1)

2K(a + d)2 2K c) d) K(a + d )2
a) 3Ma2 b) Ma2

3M

58. A single degree of freedom mass-spring-viscous damper system with mass m, spring constant

k and viscous damping coefficient q is critically damped. The correct relation among m, k and

q is (GATE-16-Set 2)

a) b) q = 2 km c) q = 2k d) q = 2 k
m m

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Previous IES Questions for Practice

1995

1 The equation of free vibrations as a system is .. + 36π2x = 0. Its natural frequency is .

X

(a) 46 Hz
(b) 3π Hz

(c) 3 Hz
(d) 6π 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 ω/ωn = √2, where ω is the frequency of excitation and ωn is the natural frequency of vibrations, then

the trans-missibility of 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 critically damped 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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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 (δ = deflection, S = stiffness, W = load)

ss

s

(a) δ = 3W / 2S W
(c) δ = 2W / 3S
(b) δ = W / 2S

(d) δ = 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

33

(c) l1+ l2 d1 + l3 d1

d2 d3

(d) l1+ l2 44
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 by which one of the following ?

(a) ω = 2k (b) ω = √ k
m
√ 3m

(c) ω = k 2k

√ 2m (d) ω =√ m

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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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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. Mω3 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 ωt 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

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

K X
M

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

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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10 If (ω/ωn) = 2 where ‘ω’ is the frequency of excitation and ‘ωn’ is the natural frequency of vibrations,
then the transmissibility of 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 critically damped 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 k2
m

(a) 1/2π√(k1-k2/m)
(b) 1/2π√k1k2 / (k1+ k2)m
(c) 1/2π√(k1 + k2/m)
(d) 1/2π√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-ξωnt sin (√1 - ξ2ωnt + φ) which is shown
graphically below:

The envelopeAhas the equation:

X A

Xsin φ ωnt
O

(a) X e (b) X sin (√(1 - ξ2))ωnt
(c ) e-ξω nt (d) X e-ξωnt

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 ωt, Vector B the displacement y = Ysin
ωt, and φ the angle between them, then the vectors C and D represent respectively.

↓ ωB

A φ↓ 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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20 An axial flow fan balanced at one speed often exhibits substantial vibrantional effects when operated at

other speeds , mainly due to

(a) primary critical speed effect (b) secondary critical speed effect

(c) unbalanced parts of the fan (d) aerodynamic unbalance

21 Two geared shafts ‘A’and ‘B’having moments of inertia ‘Ia’and ‘Ib’and angular acceleration ‘αa’and

‘αb’respectively are meshed together. ‘B’rotates at ‘G’times the speed of ‘A’. If the gearing efficiency

of the two shafts is ‘η’, then in order to accelerate ‘B’, the torque which must be applied to ‘A’will be.

(a) Iaαa + G2 Ibαbη (b) G2 Ibαb/ η
(c) Iaαa + G2 Ibαb/ η (d) G2 Iaαb/ η

22 In S.H.M, with respect to the displacement vector, the positions of Velocity vector and Acceleration

vector will be respectively. (b) 90o and 180o
(a) 180o and 90o (d) 90o and 0o
(c) 0o and 90o

23 The amplitude versus time curve of a damped-free vibration is shown in the figure.Curve labeled ‘A’is

X1 Curve A
X3
Amplitude X2 X4
Time
tp tp

(a) a logarithmic decrement curve (b) an exponentially decreasing curve
(c) a hyperbolic curve (d) a linear curve

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

List - I List - II

A. Node and mode - 1. Geared vibration

B. Equivalent inertia - 2. Damped - free vibration

C. Log decrement - 3. Forced vibration

D. Resonance - 4. Multi - rotor vibration

Codes:

ABCD

(a) 1 4 3 2

(b) 4 1 2 3

(c) 1 4 2 3

(d) 4 1 3 2

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MECHANICAL ENGINEERING

25 If a spring mass - dashpot system is subjected to

excitation by a constant harmonic force, then at response, its amplitude of vibration will be.

(a) infinity (b) inversely proportional to damping

(c) directly proportional to damping (d) decreasing exponentially with time

26 If a compression coil spring is cut into two equal parts and the parts are then used in parallel, the ratio

of the spring rate to its initial value will be.

(a) 4 times (b) 2 times

(c) ½ times (d) 1 times

27 In a forced vibration with viscous damping, maximum amplitude occurs when forced frequency is.

(a) equal to natural frequency (b) slightly less than natural frequency

(c) slightly greater than natural frequency (d) zero

28 The value of the natural frequency obtained by Rayleigh’s method.

(a) is always greater than the actual fundamental frequency.

(b) is always less than the actual fundamental frequency.

(c) depends upon the initial deflection curve chosen and may be greater than or less than the acutal

fundamental frequency.

(d) is independent of the initial deflection curve chooses

29 In a multi - rotor system of torsional vibrations, maximum number of nodes that can occur is.

(a) two (b) equal to the number of rotors plus one

(c) equal to the number of rotors (d) equal to the number of rotors minus one

30 The equation of motion for a damped viscous vibration is 3x + 9x + 27x = 0. The damping factor is.

(a) 0.25 (b) 0.50

(c) 0.75 (d) 1.00

31 A mass is suspended at the bottom of two springs in series having stiffness 10 N/mm and 5 N/mm. The

equivalent spring stiffness of the two springs is nearly.

(a) 0.3 N/mm (b) 3.3 N/mm

(c) 5 N/mm (d) 15 N/mm

32 The critical speed of a shaft is affected by the

(a) diameter and the eccentricity of the shaft (b) span and the eccentricity of the shaft

(c) diameter and the span of the shaft (d) span of the shaft

33 The equation of free vibration of a system is X + 36π2. X = 0. Its natural frequency is

(a) 6 Hz (b) 3π Hz

(c) 3 Hz (d) 6π Hz

34 Ifa spring mass dashpot system is subjected to excitation by a constant harmonic force, then at reso

nance, its

amplitude of vibration will be.

(a) Infinity

(b) inversely proportional to damping

(c) directly proportional to damping

(d) decreasing exponentially with time

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THEORY OF MACHINE

35 Consider a harmonic motion x = 1.25 sin(5t - π/6) cm. Match List - I with List - II and select the

correct answer using the codes given below the lists:

List - I - List - II
A.Amplitude (cm) 1. 5 / 2π

B. Frequency (cycle/s) - 2. 1.25
C. Phase angle (rad) - 3. 2π/5
D. Time period (s) - 4. π/6

36 The natural frequency of transverse vibration of a mass less beam of length L having a mass m attached

at its midspan is given by (EI is the flexural rigidity of the beam)

(a) (mL3 / 48EI)½ rad/s (b) (48mL3 / EI)½ rad/s

(c) (48EI /mL3 )½ rad/s (d) (3EI/mL3)½ rad/s

37 A shaft carries a weight W at the centre. The CG of the weight is displaced by an amount e from the

axis of the rotation . If y is the additional displacement of the CG from the axis of rotation due to the

centrifugal force, then the ratio of y to e (Where ωc is the critical speed of shaft and w is the

anglular speed of shaft) is given by (b) 1 / (( ωc/ω)2 - 1)
(a) 1 / (( ωc/ω)2 + 1) (d) ω / (( ωc/ω)2 - 1)
(c) ( ωc/ω)2 + 1

38 When a vehicle travels on a rough road whose undulations can be assumed to be sinusoida, the reso

nant conditions of the base excited vibrations are determined by the.

a) mass of the vehicle, stiffness of the suspension spring, speed of the vehicle, wavelength of the rough

ness curve

(b) speed of the vehicle only

(c) speed of the vehicle and the stiffness of the suspension spring.

(d) amplitude of the undulations

39 During torsional vibration of a shaft, the node is characterized by the.

(a) maximum angular velocity (b) maximum angular displacement

(c) maximum angular acceleration (d) zero angular displacement

40 Adisc of mass ‘m’and radius ‘r’is attached to a spring of stiffness ‘k’During its motion, the disc rolls

on the ground. When released from some stretched position, the center of the disc will execute

harmonic motion with a time period of .

m
k

↓

(a) 2π (√m / a k) (b) 2π (√m / k)
(c) 2π (√3m / 2k) (d) 2π (√2m / k)

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MECHANICAL ENGINEERING

41 The assumption of viscous damping in practical vibrating system is

(a) one to reality

(b) to make the resulting differential equation linear

(c) to make the resulting differential equation non-linear

(d) to make the response of the mass linear with time

42 The ratio of the maximum dynamic displacement due to a dynamic force to the deflection due to the

static force of the same magnitude is called the.

(a)displacement ratio (b) deflection ratio

(c) force factor (d) magnification factor

43 Amachine mounted on a single coil spring has a period of free vibration of T. If the spring is cut into four

equal parts and placed in parallel and the machine is mounted on them, then the period of free vibration

of the new system will become.

(a) 16 T (b) 4 T

(c) T / 4 (d) T / 16

44 Consider the following statements:

The period of oscillation of the fluid column in a U-tube depends upon the.

1. diameter of U- tube

2. length of the fluid column

3. acceleration due to gravity

Of these statements:

(a) 1,2 & 3 are correct (b) 1 & 3 are correct

(c) 1 & 2 are correct (d) 2 & 3 are correct

45 For steady - state forced vibrations, the phase lag at

resonance is (b) 45o
(a) 0o (d) 180o
(c) 90o

46 For the vibratory system shown in the given figure, the natural frequency of vibration in rad/sec is.

(a) 43.3 ↔ k1 = 150 N/
(b) 86.6 cm
(c) 100 m = 2kg
(d) 200
k2 = 150 N/
cm

47 Logarithmic decrement of a damped single degree of freedom system is δ . If the stiffness of thespring

is doubled and the mass is made half, then the logarithmic

decrement of the new system will be equal to.

(a) (1/4) δ (b) (1/2) δ

(c) δ (d) 2 δ

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48 A uniform cantilever beam undergoes transverse vibrations. The number of natural freqeuncies associ

ated with the beam is

(a) 1 (b) 10

(c) 100 (d) infinite

49 Two vibratory systems are shown in the given figures. The ratio of the natural frequency of longitudinal

vibration of the second system to that of the first is

(a) 4 k 4k
(c) 0.5 mm

(b) 2
(d) 0.25

50 The given figure shows vibrations of a mass ‘M’ isolatedby means of springs and a damper. If an
external force ‘F’( = A sin ωt) acts on the mass and the damper is not used, then.

(a) ω = √(k/M) ↔ F = A ω sin t
(b) ω = (1/2) √(k/M) M
(c) ω = 2√(k/M)
(d) ω = √(k/2M) k/2 k/2
c

51 The transmitted force through a mass - spring damper system will be greater than the transmitted

through rigid supports for all values of damping factors, if the frequency ratio (ω/ωn).

(a) more than √2 (b) less than √2

(c) equal to one (d) less than one

52 The rotor of a turbine is generally rotated at

(a) the critical speed (b) a speed much below the critical speed

(c) a speed much above the critical speed (d) a speed having no relation to critical speed

53 A viscous damping system with free vibrations will be critically damped if the damping factor is

(a) zero (b) less than one

(c) equal to one (d) greater than one

54 The equivalent spring stiffness for the system shown in the given figure (S is the spring stiffness of each

of the three springs) is

(a) S/2 SS
(b) S/3
(c) 2S/3 Rigid bar
(d) S
S
W

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MECHANICAL ENGINEERING

55 Consider the following methods.

1. Energy method

2. Equilibrium method

3. Rayleigh’s method

Which of these methods can be used for determining the natural frequency of the free vibrations?

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

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

56 Consider the following statements

1. In forced vibrations, the body vibrates under the influence of an applied force.

2. In damped vibrations, amplitude reduces over every cycle of vibration

3. In torsional vibrations, the disc moves parallel to the axis of shaft

4. In transverse vibrations, the particles of the shaft moves approximately perpendicular to the axis of

the shaft.

57 Whriling speed of shaft is the speed at which

(a) shaft tends to vibrate in longitudinal direction

(b) torsional vibration occur

(c) shaft tends to vibrate vigorously in transverse direction

(d) combination of transverse and longitudinal vibration ccurs

58 The figure shows a rigid body oscillating about the pivotA. If J is mass moment of inertial of the body

about the axis of Rotation, its natural frequency for small oscillations is Proportional to

(a) J A
(b) J2 θ

(c) 1/J
(d) 1 / √J

↓ c.g

59 The figure shows a critically damped spring-mass damper system undergoing single degree of freedom
vibrations. If m = 5 kg and k = 20N/s, the value of viscous damping coefficient is

(a) 10 Ns/m C→
(b) 20 Ns/m
(c) 4 Ns/m m
(d) 8 Ns/m k

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THEORY OF MACHINE

60 Match list- I (force transmissibility) with list - II (frequency ratio) and select the correct answer using

the codes given below the lists:

List - I List - II
A. 1 - 1. ( ω/ωn) > √2
B. Less than 1 - 2. ( ω/ωn) = √2
C. Greater than 1 - 3. ( ω/ωn) >> √2
D. Tending to zero- 4. ( ω/ωn) < √2

Codes:

ABCD

(a) 1 2 3 4

(b) 2 1 3 4

(c) 2 1 4 3

(d) 1 2 4 3

61 Asystem is shown in the following figure. The barAB is assumed to be rigid and weightless. The natural
frequency of vibration of the system is given by.

a→→
→
k1

B

l→

k2

m

(a) fm = (1/2π) (√k1k2(a / l)2)/ (m(k2+(a / l)2k1)
(b) fm = (1/2π) (√k1k2)(mk1+k2)
(c) fm = (1/2π) (√(k1) (mk2)
(d) fm = (1/2π) (√k1+ k2 /(mk2k1)

“The most powerful weapon on earth is the human soul on fire”

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MECHANICAL ENGINEERING

Answers :-
CLASS ROOM OBJECTIVE :
1-a, 2-a, 3-a, 4-b, 5-a, 6-d, 7-b, 8-d, 9-sol., 10-b, 11-a, 12-b, 13-greater, 14-d, 15-b, 16-b, 17-sol,
18-c, 19-d, 20-d, 21-c, 22-c, 23-a, 24-a, 25-c, 26-a, 27-b, 28-a, 29-a, 30-b, 31-b, 32-c, 33-6.32, 34-
0.4, 35-c, 36-20, 37-100

Two Marks Ans. :
38-a, 39-a, 40-c, 41-a, 42-d, 43-c, 44-0.0658, 45-d, 46-d, 47-1.25, 48-10, 49-2.28, 50-d, 51-b, 52-
6767.7, 53-b, 54-a, 55-10, 56-0.5, 57-a, 58-b

PREVIOUS IES QUESTIONS FOR PRACTICE
1 - c , 2 - a, 3 - b, 4 - c, 5 - a , 6 - b, 7 - a, 8 - d, 9 - c, 10 - a, 11 - a ,12 - d,13 - a , 14 - a, 15 - c, 16
- b, 17 - c , 18 - a, 19 - a,

ADDITIONAL OBJECTIVES FOR PRACTICE
1 - b , 2 - b, 3 - c, 4 - a, 5 - c, 6 - d , 7 - a, 8 - c, 9 - b, 10 - b, 11 - b,12 - a, 13 - b, 14 - a ,15 - c,16
- a , 17 - d, 18 - a, 19 - c, 20 - a , 21 - c, 22 - b, 23 - c, 24 - b, 25 - b, 26 - , 27 - b, 28 - a, 29 - d,
30 - b,31 - b, 32 - c, 33 - c, 34 - b, 35 - d,36 - c, 37 - b, 38 - a , 39 - d, 40 - c, 41 - a,b, 42 - d,43 - c,
44 - d, 45 - c, 46 - c , 47 - c, 48 - d, 49 - b, 50 - a,51 - b , 52 - c, 53 - c, 54 - c, 55 - b, 56 - d , 57 - c,
58 - c, 59 - b, 60 - c, 61 - a,

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5 GOVERNORS

1. A Hartnell governor has its controlling force F given F = P + qr, where r is the radius of the balls and

p and q are constants. (ESE-93)

(a) p = 0 and q is positive

(b) p is positive and q = 0

(c) p is negative and q is positive

(d) p is positive and q is also positive

2. The plots of controlling force versus radii of rotation of the balls of spring controlled governors are
shown in the given diagram.Astable governor is characterized by the curve labeled. (ESE-93)

(a) I

(b) II

(c) III

(d) IV

3. A spring controlled governor is found unstable. It can be made stable by (ESE-94)
(a) increasing the spring stiffness
(b) decreasing the spring stiffness
(c) increasing the ball weight
(d) decreasing the ball weight

4. Match List - I with List - II and select the correct answer: (ESE-96)

List - I CD
13
A. Hunting B. Isochronism 43
43
C. Stability D. Effort 34

List - II

1. One radius rotation for each speed

2. Too sensitive

3. Mean force exerted at the sleeve during change of speed

4. Constant equilibrium speed for radii of rotation

Codes: A B

(a) 2 4

(b) 3 1

(c) 2 1

(d) 1 2

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5. Which one of the following equation is valid with reference to the given figure? (ESE-96)

(a) ω2 = W g
w h

(b) ω2 = W + w 1
w
g2

h

(c) ω2 = w 1
W+w
h2

g

(d) ω2 = W + w g
w h

6. Assertion (A) : The degree of hunting with an unstable governor will be less than with an isochronous
governor.
Reason (R) : With an unstable governor, once the sleeeve has moved from one extreme position to
the other, a finite change of speed is required to cause it to move back again. (ESE-97)
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not a correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

7. The sensitivity of an isochronous governor is (ESE-97)
(a) zero
(c) two (b) one
(d) infinity

8. Which of the following pair (s) is/are correctly matched? (ESE-98)

I. Four bar chain - Oscillating-converter

II. Intertia governor - Rate of change of engine speed

III. Hammer blow - Reciprocating unbalance

Select the correct answer using the codes given below:

(a) I alone (b) I, II and III

(c) II and III (d) I and II

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THEORY OF MACHINE

9. Given that (ESE - 98)
2g
m = mass of the ball of the governor,
ω = angular velocity of the governor and (d) ω2
g = accelerate due to gravity

The height of Watt’s governor is given by

g g √2g
(a) 2ω2 (b) ω2 (c) ω2

10. For a given fractional change of speed, if the displacement of the sleeve is high, then the governor is said

to be (ESE - 98)

(a) Hunting (b) Isochronous

(b) Sensitive (d) Stable

11. Consider floolwing figure (ESE-99)

Assertion (A) : In order to have the same equilibrium speed for the given values of w, W and h, the masses
of balls used in the proell governor are less than those of balls used in the Porter governor.

Reason (R) : The ball is fixed to all extension link in Proell governor.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not a correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

12. Consider the following speed governors :
1. Porter governor
2. Hartnell governor
3. Watt governor
4. Proell governor

The correct sequence of development of these governors is (ESE -99)

(a) 1.3.2.4 (b) 3.1.4.2

(c) 3.1.2.4 (d) 1.3.4.2

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MECHANICAL ENGINEERING

13. Sensitiveness of a governor is defined as (ESE-00)

(a) Range of speed
2 x Mean speed

(b) Mean speed
Range of speed

(c) Mean speed x Range of speed.

(d) Range of speed
Mean speed

14. The nature of the governors is shown by the graph between radius (r) of rotation and controlling

force (F). Which of the following is an isochronous governor? (ESE-02)

15. In a Hartnell governor, the mass of each ball is 2.5 kg. Maximum and minimum speeds of rotation are

10 rad/s and 8 rad/s respectively. Maximum and minimum radii of rotation are 20 cm and 14 cm

respectively. The lengths of horizontal and vertical arms of bell crank levers are 10 cm and 20 cm

respectively. Neglecting obliquity and gravitational effects, the lift of the sleeve is (ESE-02)

(a) 1.5 cm (b) 3.0 cm

(c) 6.0 cm (d) 12.0 cm

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THEORY OF MACHINE

16. For minimizing speed fluctuations of an engine as a prime mover, it must have (ESE-03)

(a) Only a flywheel fitted to the crankshaft

(b) governor provided in the system

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

(d) Neither a flywheel nor a governor

17. Effect of friction at the sleeve of a centrifugal governor is to make it (ESE-03)

(a) More sensitive

(b) More stable

(c) Insensitive over a small range of speed

(d) Unstable

18. Consider the following statement : (ESE-03)

1. Flywheel and governor of an engine are the examples of an open loop control system

2. Governor is the example of closed loop control system

3. The thermostat of a refrigerator and relief valye of a boiler are examples of closed loop control

system

Which of these statements is/are correct? (ESE-03)

(a) 1 only (b) 2 and 3

(c) 3 only (d) 2 only

19. Which one of the following statements is correct? (ESE-04)

A governor will be stable if the radius of rotaion of the balls

(a) increases as the equilibrium speed decreases

(b) decreases as the equilibrium speed increases

(c) increases as the equilibrium speed increases

(d) remains unaltered with the change in equilibrium speed

20. Which one of the following governors is used to drive a gramophone? (ESE-05)

(a) Watt governor

(b) Porter governor

(c) Pickering Governor

(d) Hartnell governor

21. Consider the following statements concerning centrifugal governors:

1. The slope of the controling force curve should be less than that of the straight line representing the

centripetal force at the speed considered for the stability of centrifugal governor

2.Isochronisms for a centrifugal governor can be achieved only at the expense of stability

3. When sleeve of a centrifugal governor reaches its topmost position the engine should develop

maximum power.

Which of the statements given above is/are correct?

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

(c) 2 only (d) 3 only (ESE-05)

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MECHANICAL ENGINEERING (ESE-05)

22. Which one of the following expresses the sensitiveness of a governor ?
a) b)

c) d) 2(N1-N2 )
N1 N 2

(Where N1 = Maximum equilibrium speed, N2 = Minimum Equilibrium speed)

23. The controlling forc curves for a spring controlled govenor are shown in the above figure. Which curve

represents a stable governor ? (ESE-07)

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

24. For a governor running at constant speed, what is the value of the force acting on the sleeve ?
(ESE-07)

a) Zero
b) Variable depending upon the load
c) Maximum
d) Minimum

25. In a Hartnell govenor, the mass of each ball is 2.5 kg. Maximum and minimum centrifugal force on the

balls are 2000 N and 1000 N corresponding to radit 20 cm and 15 cm respectively. Length of vertical

and horizontal arms of the bell-crank levers are the same, then what is the spring stiffness in N/cm ?

a) 100 b) 200 c) 400 d) 800

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26. Cosider the following statements: (ESE-09)

A governor is said to be

1. Sensitive when it readily respond to small change in speed

2. isochronous if it has no sensitivity

3. hunting if it is too sensitive

Which of the above statements is/are true?

(a) 1 ony (b) 1 and 2

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

27. The function of the governor is (ESE-12)

a) To limit the fluctuations of speed during each cycle

(b) To maintain the supply of fuel to the engine cycle constant when the load on the engine varies

(c) To maintain constant speed of rotation of the crank shaft when the load on the engine varies

(d) To maintain constant speed of rotation of the crank shaft when the load on the engine is constant

28. Statement (I):If a centrifugal governor is stable at a particular position, it would be stable at all other

position in the working range of operation.

Statement (II): Porter governor is a stabale governor throughout its range of operation

(a) Both Statement (I) and Statement (II) are individually true and statement (II) is the correct explanation

of Statement (I)

(b) Both statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct

explation of Statement (I)

(c) Statement (I) is true but Statement (II) is false

(d) Statement (I) is false but Statement (II) is true (ESE-13)

29. In a centrifugal governor, the controlling force is observed to be 14 N when the radius of rotation

is 2 cm and 38 N when the radius of rotation is 6 cm, the governor: (ESE-13)

(a) is a stable governor

(b) is an unstable govenor

(c) is an isochronous governor

(d) cannot be said of what type with the given data

30. In a Watt governor the weight of the ball is 50 N and the friction at the sleeve is 10 N. The coefficient

of detention would be: (ESE-13)

(a) 5.0 (b) 0.5 (c) 0.2 (d) 0.1

31. The sleeve and each rotating mass of a porter governor weigh respectively, 200 N and 50 N. If the

friction at the sleeve is 10 N then the coeffcient of detention would be: (ESE-13)

(a) 0.20 (b) 0.40 (c) 0.04 (d) 0.05

32. The governor is said to be stable when: (ESE-13)

(a) For each speed within the working range there is only one radius of rotation for the governor ball

(b) The equilibrium speed is constant for all radii rotation of the balls within working range.

(c) There is a slightest increase in speed, the governor balls will fly to this maximum radius.

(d) The governor admits either maximum of minimum amout of energy to the engine and will not admit

an amount of energy between these two extremes.

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MECHANICAL ENGINEERING

33. When the speed of the engine fluctuate continuously above the below the mean speed, then the

governor is said to be: (ESE-13)

(a) Stable

(b) Unstable

(c) Isochronous

(d) Hunting

34. The governor becomes isochronus, when (ESE-14)

(a) F = ar + b

(b) F = ar - b

(c) F = ar2 +b

(d) F = ar

35. The sensitiveness of governor is defined as

(a) N1- N2 (b) N1+ N2
N1+N2 N1- N2

(c) (N1+N2) (d) (N1-N2)
N1-N2 N1+N2

Were N1 and N2 are the maximum equilibrium speed of the governor respectively?

36. In a governor, if the equilibrium speed is constant for all radii of rotatin of balls, the governor is said to
be (ESE-14)
(a) stable
(b) unstable
(c) inertial
(d) isochronous

37. A governor is said to be isochronous when the equilibrium speed is (ESE-15)
(a) variable for different radit of rotation of governor balls
(b) constant for all radio of rotation of the balls within the working range
(c) constant for particular radie of rotation of governor balls
(d) constant for only one radius of rotation of governor balls

38. The power of a governor is the work done at (ESE-15)
(a) the governor balls for change of speed
(b) the sleeve for zero change of speed
(c) the sleeve for a given rate of change of speed
(d) each governor ball for given percentage change of speed

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THEORY OF MACHINE

39. Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated in the
plane of the paper about point P lying 5 mm away from its centre. The radius of the cam is 20 cm. The
distance (in mm) between the highest and the lowest positions of the flat face follower is
(GATE-PI-16)

a) 5 b)10 c) 40 d) 45
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“The art of being wise is the art of knowing what to overlook”

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

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