TOM Objective

THEORY OF MACHINE

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 ‘a’and

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

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

(a) Iaa + G2 Ibb (b) G2 Ibb/ 
(c) Iaa + G2 Ibb/  (d) G2 Iab/ 

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

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) inverselyproportional 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) slightlyless 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 + 362. X = 0. Its natural frequency is

(a) 6 Hz (b) 3 Hz

(c) 3 Hz (d) 6 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 - /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 / 2

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

36 The natural frequencyof 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 c is the critical speed of shaft and w  is the

anglular speed of shaft) is given by

(a) 1 / (( c/)2 + 1) (b) 1 / (( c/)2 - 1)
(c) ( c/)2 + 1 (d)  / (( c/)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) 2 (m / a k) (b) 2 (m / k)
(c) 2 (3m / 2k) (d) 2 (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
(d) 200 m = 2kg

k2 = 150 N/
cm

47 Logarithmic decrement of a damped single degree of freedom system is  . 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)  (b) (1/2) 
(c)  (d) 2 

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THEORY OF MACHINE

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 vibratorysystems 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 t) acts on the mass and the damper is not used, then.

(a) = (k/M)  F = A sin t
(b) = (1/2) (k/M)
(c) = 2(k/M) M
(d)= (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 (/n).

(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 

(c) 1/J
(d) 1 / J

 c.g

59 The figure shows a criticallydamped 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. ( /n) > 2
B. Less than 1 - 2. ( /n) = 2
C. Greater than 1 - 3. ( /n) >> 2

D. Tending to zero- 4. ( /n) < 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 = (1/2) (k1k2(a / l)2)/ (m(k2+(a / l)2k1)
(b) fm = (1/2) (k1k2)(mk1+k2)
(c) fm = (1/2) ((k1) (mk2)
(d) fm = (1/2) (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

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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THEORY OF MACHINE

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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MECHANICAL ENGINEERING

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

(a) 2 = W g
w h

(b) 2 = W + w 1
w
g2

h

(c) 2 = w 1
W+w
h2

g

(d) 2 = 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 Aand 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) Ais true but R is false
(d) Ais 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,
angular velocity of the governor and (d) 2
g = accelerate due to gravity

The height of Watt’s governor is given by

g g 2g
(a) 22 (b) 2 (c) 2

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 Aand 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) Ais true but R is false
(d) Ais 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 (ESE-00)

13. Sensitiveness of a governor is defined as
Range of speed

(a) 2 x Mean speed
Mean speed

(b) Range of speed

(c) Mean speed x Range of speed.
Range of speed

(d) 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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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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22. Which one of the following expresses the sensitiveness of a governor? (ESE-05)

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

2N1+N2 2N1N2

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

2 N -N N +N
12 12

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

23. The controlling forc curves for a spring controlled governor 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 governor, the mass of each ball is 2.5 kg. Maximum and minimum centrifugal forces on the

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

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

(ESE-09)

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

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THEORY OF MACHINE

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 individuallytrue 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 energyto the engine and will not admit

an amount of energy between these two extremes.

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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) N - N (b) N + N
12 12
N1+N2 N1- N2

(c) (N +N ) (d) (N -N )
12 12
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

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

“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

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