## Applied Mechanics Multiple Choice Questions

1. A projectile is thrown at an angle a to the horizontal with α velocity v. It will have the maximum centripetal acceleration

A. at the start
B. at the top of the trajectory
C. as it strikes the ground
D. else where.

2. A cable loaded with 0.5 tonne per horizontal metre span is stretched between supports in the same horizontal line 400 m apart. If central dip is 20 m, the minimum tension in the cable, will be

A. 200 tonnes at the centre
B. 500 tonnes at the centre
C. 200 tonnes at the right support
D. 200 tonnes at the left support.

3. The Law of Polygon of Forces states that

A. if a polygen representing the forces acting at point in a body is closed, the forces are in equilibrium
B. if forces acting on a point can be represented in magnitde and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by the closing side of the polygon
C. if forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side of the polygon, taken in opposite order
D. if forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium.

4. The centre of gravity of a triangle is at the point where three

A. medians of the triangle meet
B. perpendicular bisectors of the sides of the triangle meet
C. bisectors of the angle of the triangle meet
D. none of these.

5. The forces which meet at one point and have their lines of action in different planes are called

A. coplaner non-concurrent forces
B. non-coplaner concurrent forces
C. non-coplaner non-current forces
D. intersecting forces
E. none of these.

6. At a given instant ship A is travelling at 6 km/h due east and ship B is travelling at 8 km/h due north. The velocity of B relative to A is

A. 7 km/hrs
B. 2 km/hrs
C. 1 km/hrs
D. 10 km/hrs
E. 14 km/hrs.

7. The locus of the instantaneous centre of a moving rigid body, is

A. straight line
B. involute
C. centroid
D. spiral.

8. If a body moves in such a way that its velocity increases by equal amount in equal intervals of time, it is said to be moving with

A. a uniform retardation
B. a uniform acceleration
C. a variable acceleration
D. a variable retardation
E. none of these.

9. If the gravitational accelerational at any place is doubled, the weight of a body, will

A. be reduced to half
B. be doubled
C. not be affected
D. none of these.

10. Parallelogram Law of Forces states, “if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by

A. its longer side”
B. its shorter side”
C. the diagonal of the parallelogram which does not pass through the point of intersection of the forces”
D. the diagonal of the parallelogram which passes through the point of intersection of the forces”
E. half the sum of the diagonals”.

11. Which one of the following statements is true ?

A. The tangent of the angle of friction is equal to coefficeint of friction
B. The angle of repose is equal to angle of friction
C. The tangent of the angle of repose is equal to coefficient of friction
D. All the above.

12. The product of mass and velocity of a moving a body, is called

A. moment
B. momentum
C. power
D. impulse.

13. Engineer’s units of force, is

A. Newton in absolute units
B. Dyne in absolute units
C. Newton and dyne in absolute units
D. All the above.

14. Joule is the unit of

A. work
B. force
C. power
D. torque
E. none of these.

15. The maximum velocity of a body vibrating with a simple harmonic motion of amplitude 150 mm and frequency 2 vibrations/sec, is

A. 188.5 m/sec
B. 18.85 m/sec
C. 1.885 m/sec
D. 0.18845 m/sec.

16. The angle which an inclined surface makes with the horiontal when a body placed on it is on the point of moving down, is called

A. angle of repose
B. angle of friction
C. angle of inclination
D. none of these.

17. Work may be defined as

A. force x distance
B. force x velocity
C. force x acceleration
D. none of these.

18. A bullet weighing 200 g is fired horizontally with a velocity of 25 m/sec from a gun carried on a carriage which together with the gun weighs 100 kg. The velocity of recoil of the gun, will be

A. 0.01 m/sec
B. 0.05 m/sec
C. 1.00 m/sec
D. 1.5 m/see.

19. The tension in a cable supporting a lift

A. is more when the lift is moving downwards
B. is less when the lift is moving upwards
C. remains constant whether its moves downwards or upwards
D. is less when the lift is moving downwards.

20. A satellite moves in its orbit around the earth due to

A. Gravitational force
B. Centripetal force
C. Centrifugal force
D. none of these.

21. If three rigid rods are hinged together to form a triangle and are given rotary as well as translatory motion, the number of instantaneous centres of the triangle, will be

A. 1
B. 2
C. 3
D. 4
E. 5.

22. The mechanical advantage of an ideal machine is 100. For moving the local through 2 m, the effort moves through

A. 0.02 m
B. 2 m
C. 2.5 m
D. 20 m.

23. When a body in equilibrium undergoes an infinitely small displacement, work imagined to be done, is known as

A. imaginary work
B. negative work
C. virtual work
D. none of these.

24. To attain the synchronous orbit, the launch of a satellite, is done from a place

A. on equator
B. on 30° latitude
C. on 45° latitude
D. on 60° latitude
E. on the poles.

25. Pick up the correct statement from the following :

A. Nature plays an important role in the launch of a satellite
B. The earth’s gravity reduces the speed of a satellite by 32 km per second
C. The gravitational force relents as the satellite climbs higher
D. The gravitational intensity declines with height
E. All the above.

26. If the radius of the earth is 600 km the height of a mountain above sea level at the top of which a beat seconds pendulum at sea level, looses 27 seconds a day, is

A. 500 metres
B. 1000 metres
C. 1500 metres
D. 2000 metres
E. 25000 metres.

27. The total time of collision and restitution of two bodies, is called

A. time of collision
B. period of collision
C. period of impact
D. all the above.

28. The length of a Second’s pendulum, is

A. 99.0 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
E. 101.10 cm.

29. A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The efficiency of the lifting machine is

A. 50%
B. 40%
C. 55%
D. 30%.

30. A string of length 90 cm is fastened to two points A and B at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force P is applied to the ring such that it is in equilibrium vertically below B. The value of P is :

A. 40 g
B. 60 g
C. 80 g
D. 100 g.

31. Two forces act an angle of 120°. If the greater force is 50 kg and their resultant is perpendicular to the smaller force, the smaller force is

A. 20 kg
B. 25 kg
C. 30 kg
D. 35 kg
E. 40 kg.

32. A uniform rod 9 m long weighing 40 kg is pivoted at a point 2 m from one end where a weight of 120 kg is suspended. The required force acting at the end in a direction perpendicular to rod to keep it equilibrium, at an inclination 60° with horizontal, is

A. 40 kg
B. 60 kg
C. 10 kg
D. 100 kg.

33. If a particle is projected inside a horizontal tunnel which is 554 cm high with a velocity of 60 m per sec, the angle of projection for maximum range, is

A. 8°
B. 9°
C. 10°
D. 11°
E. 12°.

34. Newton’s law of Collision of elastic bodies states that when two moving bodies collide each other, their velocity of separation

A. is directly proportional to their velocity of approach
B. is inversely proportional to their velocity of approach
C. bears a constant ratio to their velocity of approach
D. is equal to the sum of their velocities of approach.

35. Two forces of 6 Newtons and 8 Newtons which are acting at right angles to each other, will have a resultant of

A. 5 Newtons
B. 8 Newtons
C. 10 Newtons
D. 12 Newtons.

36. A projectile is fired with a velocity of 100.3 m/sec. at an elevation of 60°. The velocity attained by the projectile when it is moving at a height of 100 m, is

A. 70 m/sec.
B. 75 m/sec.
C. 80 m/sec.
D. 85 m/sec.
E. 90 m/sec.

37. The following factor affects the orbit of a satellite up to an altitude of 720 km from the earth’s surface

A. uneven distribution of the gravitational field
B. gravity of the sun and the moon
C. aerodynamic forces
D. none of these.

38. A body is said to move with Simple Harmonic Motion if its acceleration, is

A. always directed away from the centre, the point of reference
B. proportional to the square of the distance from the point of reference
C. proportional to the distance from the point of reference and directed towards it
D. inversely proportion to the distance from the point of reference
E. none of these.

39. One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The reaction between the sphere and the wall of the arrangement made is

A. 102.5 kg
B. 105.5 kg
C. 108.5 kg
D. 110 kg.

40. Which one of the following laws is not applicable to a simple pendulum ?.

A. The time period does not depend on its magnitude
B. The time period is proportional to its length l
C. The time period is proportional to l where l is length
D. The time period is inversely proportional to g where g is the acceleration due to gravity.

41. Effect of a force on a body depends upon its

A. direction
B. magnitude
C. position
D. all the above.

42. A Seconds pendulum executes

A. 0.5 beat per second
B. 1.0 beat per second
C. 2.0 beats per second
D. 2.5 beats per second
E. 3 beats per second.

43. The resultant of the forces acting on a body will be zero if the body

A. rotates
B. moves with variable velocity in a straight line
C. moves along a curved path
D. does not move at all.

44. A ball moving with a velocity of 5 m/sec impinges a fixed plane at an angle of 45° and its direction after impact is equally inclined to the line of impact. If the coefficient of restitution is 0.5, the velocity of the ball after impact will be

A. 0.5 m/sec
B. 1.5 m/sec
C. 2.5 m/sec
D. 3.5 m/sec
E. 4.5 m/sec.

45. A particle moves with a velocity of 2 m/sec in a straight line with a negative acceleration of 0.1 m/sec2. Time required to traverse a distance of 1.5 m, is

A. 40 sec
B. 30 sec
C. 20 sec
D. 15 sec
E. 10 sec.

46. For maximum range of a projectile, the angle of projection should be

A. 30°
B. 45°
C. 60°
D. none of these.

47. According to Law of Triangle of Forces

A. three forces acting at a point, can be rep-resented by the sides of a triangle, each side being in proportion to the force
B. three forces acting along the sides of a triangle are always in equilibrium
C. if three forces acting on a, point can be represented.in magnitude and direction, by the sides of a triangle taken in order, these will be in equilibrium
D. if three forces acting at a point are in equilibrium each force is proportional to the sine of the angle between the other two
E. if the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third side of the triangle, taken in opposite order.

48. A Second’s pendulum gains 2 minutes a day. To make it to keep correct time its length

A. must be decreased
B. must be increased
C. is not changed but weight of the bob is increased
D. is not changed but weight of the bob is decreased
E. none of these.

49. The following is not a law of static friction :

A. The force of friction always acts in a direction opposite to that in which the body tends to move
B. The force of friction is dependent upon the area of contact
C. The force of friction depends upon the roughness of the surface
D. The magnitude of the limiting friction bears a constant ratio to the normal reaction between two surfaces.

50. The velocity of a moving body, is

A. a vector quantity
B. a scalar quantity
C. a scalar as well as a vector quantity
D. none of these.

51. The resolved part of the resultant of two forces inclined at an angle θ in a given direction is

A. algebraic sum of the resolved parts of the forces in the direction
B. arithmetical sum of the resolved parts of the forces in the direction
C. difference of the forces multiplied by cosine θ°
D. sum of the forces multiplied by the sine θ
E. sum of the forces multiplied by the tangent θ°.

52. The following statement is one of the laws of Dynamic friction

A. The force of friction always acts in a direction opposite to that in which a body is moving
B. The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
C. For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed
D. all the above.

53. A 50 kg boy climbs up a 8 m rope in gymnasiam in 10 sec. The average power developed by the boy is approximately

A. 400 watts
B. 500 watts
C. 4000 watts
D. none of these.

54. Lami’s theroem states that

A. three forces acting at a point are always in equilibrium
B. if three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
C. three coplaner forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
D. three coplaner forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
E. none of these.

55. Pick up the incorrect statement from the following. In case of suspension bridge due to rise in temperature,

A. dip of the cable increases
B. length of the cable increases
C. dip of the cable decreases
D. none of the these.

56. If two forces acting at a point are in equilibrium, they must be equal in magnitude and their line of action must be along

A. the same line in the same sense
B. the same line in opposite sense
C. the perpendicular to both the lines
D. none of these.

57. For lifting a load of 50 kg through a distance of 2.5 cm, an effort of 12.5 kg is moved through a distance of 40 cm. The efficiency of the lifting machine, is

A. 60%
B. 65%
C. 70%
D. 25%.

58. Power can be expressed as

A. work/energy
B. work/time
C. work x time
D. work/distance.

59. To avoid bending action at the base of a pier,

A. suspension and anchor cables are kept at the same level
B. suspension and anchor cables are fixed to pier top
C. suspension cable and anchor cables are attached to a saddle mounted on rollers on top of the pier
D. none the these.

60. If the angle between the applied force and the direction of motion of a body, is between 90° and 180°, the work done, is called

A. virtual work
B. imaginary work
C. zero work
D. negative work.

61. For a body moving with simple harmonic motion, the number of cycles per second, is known as its

A. oscillation
B. amplitude
C. periodic time
D. beat
E. frequency.

62. If the horizontal range is 2.5 times the greatest height, the angle of projection of the projectile, is

A. 57°
B. 58°
C. 59°
D. 60°.

63. The shape of a suspended cable under its own weight, is

A. parabolic
B. circular
C. catenary
D. elliptical.

64. Time required to stop a car moving with a velocity 20 m/sec within a distance of 40 m, is

A. 2 sec
B. 3 sec
C. 4 sec
D. 5 sec
E. 6 sec.

65. The characteristic of a couple, is :

A. algebraic sum of forces, constituting a couple is zero
B. algebraic sum of moments of forces, constituting a couple, about any poin, is same
C. a couple can be balanced only by a couple but of opposite sense
D. a couple can be never the balanced by a single force
E. all the above.

66. One end of a light string 4 m in length is fixed to a point on a smooth wall and the other end fastened to a point on the surface of a smooth sphere of diameter 2.25 m and of weight 100 kg. The tension in the string is

A. 17.5 kg
B. 19.5 kg
C. 22.5 kg
D. 25 kg.

67. The inherent property of a body which offers reluctance to change its state of rest or uniform motion, is

A. weight
B. mass
C. interia
D. momentum.

68. Ball A of mass 250 g moving on a smooth horizontal table with a velocity of 10 m/s hits an identical stationary ball B on the table. If the impact is perfectly elastic, the velocity of the ball B just after impact would be

A. zero
B. 5 m/sec
C. 10 m/sec
D. none of these.

69. A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The velocity ratio of the lifting machine is

A. 50
B. 55
C. 60
D. 65
E. 70.

70. The angle of friction is :

A. The ratio of the friction and the normal reaction
B. The force of friction when the body is in motion
C. The angle between the normal reaction and the resultant of normal raction and limiting friction
D. The force of friction at which the body is just about to move.

71. For perfectly elastic bodies, the value of coefficient of restitution is

A. zero
B. 0.5
C. 1.0
D. between 0 and 1.

72. The motion of a particle is described by the relation x = t2- 10t + 30, where x is in metres and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be

A. zero
B. 30 m
C. 50 m
D. 60 m
E. none of these.

73. Three forces which act on a rigid body to keep it in equilibrium. The forces must be coplanar and

A. concurrent
B. parallel
C. concurrent parallel
D. none of these.

74. Two shots fired simultaneously from the top and bottom of a vertical tower with elevations of 30° and 45° respectively strike a target simultaneously. If horizontal distance of the target from the tower is 1000 m, the height of the tower is

A. 350 m
B. 375 m
C. 400 m
D. 425 m.

75. The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is

A. 1/4
B. 1/2
C. 3/4
D. 2.

76. The apparent weight of a man in a moving lift is less than his real weight when it is going down with

A. uniform speed
B. an acceleration
C. linear momentum
D. retardation.

77. P is the force acting on a body whose mass is m and acceleration is f. The equation P – mf = 0, is known as

A. equation of dynamics
B. equation of dynamic equilibrium
C. equation of statics
D. none of these.

78. A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,

A. 5 N
B. 10 N
C. 15 N
D. 25 N
E. None of these.

79. Newtons’s Law of Motion is :

A. Every body continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force
B. The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
C. To every action, there is always an equal and opposite reaction
D. All the above.

80. The equation of motion of a particle starting from rest along a straight line is x = t3 – 3l2 + 5. The ratio of the velocities after 5 sec and 3 sec will be

A. 2
B. 3
C. 4
D. 5
E. 4.5

81. The necessary condition of equilibrium of a body, is :

A. algebraic sum of horizontal components of all the forces must be zero
B. algebraic sum of vertical components of all the forces must be zero
C. algebraic sum of the moments of the forces about a point must be zero
D. all (a), (b) and (c).

82. Two particles have been projected at angles 64° and 45° to the horizontal. If the velocity of projection of first is 10 m/sec, the velocity of projection of the other for equal horizontal ranges is

A. 9.3 m/sec
B. 8.3 m/sec
C. 7.3 m/sec
D. 6.3 m/sec.

83. A trolley wire weighs 1 kg per metre length. The ends of the wire are attached to two poles 20 m apart. If the horizontal tension is 1000 kg, the central dip of the cable is

A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm.

84. Principle of Transmissibility of Forces states that, when a force acts upon a body, its effect is

A. maximum if it acts at the centre of gravity of the body
B. different at different points on its line of
C. same at every point on its line of action
D. minimum if it acts at the C.G. of the body
E. none of these.

85. A ball is dropped from a height of 2.25 m on a smooth floor and rises to a height of 1.00 m after the bounce. The coefficient of restitution between the ball and the floor is

A. 0.33
B. 0.44
C. 0.57
D. 0.67

86. If the linear velocity of a point on the rim of a wheel of 10 m diameter, is 50 m/sec, its angular velocity will be

87. The force acting on a point on the surface of a rigid body may be considered to act

A. at the centre of gravity of the body
B. on the periphery of the body
C. on any point on the line of action of the force
D. at any point on the surface normal to the line of action of the force.

88. A satellite is said to move in a synchronous orbit if it moves at an altitude of 36, 000 km with a maximum velocity of about

A. 7000 km per hour
B. 8000 km per hour
C. 9000 km per hour
D. 10, 000 per hour
E. 11, 000 km per hour.

89. A marble ball is rolled on a smooth floor of a room to hit a wall. If the time taken by the ball in returning to the point of projection is twice the time taken in reaching the wall, the coefficient of restitution between the ball and the wall, is

A. 0.25
B. 0.50
C. 0.75
D. 1.0

90. A number of forces acting simultaneously on a particle of a body

A. may not be replaced by a single force
B. may be replaced by a single force
C. may be replaced by a single force through C.G. of the body
D. may be replaced by a couple
E. none of these.

91. A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be

A. 10 m/sec
B. 15 m/sec
C. 20 m/sec
D. 25 m/sec.

92. Pick up the correct statement from the following. A rubber ball when strikes a wall rebounds but a lead ball of same mass and velocity when strikes the same wall, falls down

A. rubber and lead balls undergo equal changes in momentum
B. change in momentum suffered by lead ball is less that of rubber ball
C. momentum of rubber ball is less than that of lead ball
D. none of these.

93. The instantaneous centre of a member lies at the point of intersection of two lines drawn at the ends of the member such that the lines are inclined to the direction of motion of the ends at

A. 30°
B. 45°
C. 60°
D. 90°

94. A retarding force on a body does not

A. change the motion of the body
B. retard the motion of the body
C. introduce the motion of the body
D. none of these.

95. The unit of force in C.G.S. system of units, is called

A. dyne
B. Newton
C. kg
D. all the above.

96. A block of weight 50 kg is placed on a horizontal plane. When a horizontal force of 18 kg is applied, the block is just on the point of motion. The angle of friction is

A. 17° 48′
B. 18° 48′
C. 19° 48′
D. 20° 48′
E. 21° 48′.

97. From a circular plate of a diameter 6 cm is cut out a circle whose diameter is equal to the radius of the plate. The C.G. of the remainder from the centre of circular plate is at a distance of

A. 2.0 cm
B. 1.5 cm
C. 1.0
D. 0.5 cm.

98. The force which produces an acceleration of 1 m/sec2 in a mass of one kg, is called

A. dyne
B. Netwon
C. joule
D. erg.

99. A sphere is resting on two planes BA and BC which are inclined at 45° and 60° respectively with the horizontal. The reaction on the plane BA will be

A. less than that on BC
B. more than that of BC
C. equal to that on BC
D. zero
E. none of these.

100. A projectile is fired at an angle θ to the vertical. Its horizontal range will be maximum when θ is

A. 0°
B. 30°
C. 45°
D. 60°
E. 90°.

101. A load of 500 kg was lifted through a distance of 13 cm. by an effort of 25 kg which moved through a distance of 650 cm. The mechanical advantage of the lifting machine is

A. 15
B. 18
C. 20
D. 26.

101. One half of a vibration of a body, is called

A. period time
B. oscillation
C. beat
D. amplitude.

102. On a ladder resisting on a smooth ground and leaning against a rough vertical wall, the force of friction acts

A. towards the wall at its upper end
B. away from the wall at its upper end
C. upwards at its upper end
D. downwards at its upper end
E. none of these.

103. The acceleration of a particle moving along the circumference of a circle with a uniform speed, is directed

B. tangentially at that point
C. away from the centre
D. towards the centre.

104. From the circular plate of a diameter 6 cm is cut out a circular plate whose diameter is equal to radius of the plate. The c.g. of the remainder shifts from the original position through

A. 0.25 cm
B. 0.50 cm
C. 0.75 cm
D. 1.00 cm.

105. In simple harmonic motion, acceleration of a particle is proportional to

A. rate of change of velocity
B. displacement
C. velocity
D. direction
E. none of these.

106. A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if

A. floor is smooth and the wall is rough
B. floor is rough and the wall is smooth
C. floor and wall both are smooth surfaces
D. floor and wall both are rough surfaces.

107. In a simple screw jack, the pitch of the screw is 9 mm and length of the handle operating the screw is 45 cm. The velocity ratio of the system is

A. 1.5
B. 5
C. 25
D. 314

108. To double the period of oscillation of a simple pendulum

A. the mass of its bob should be doubled
B. the mass of its bob should be quadrupled
C. its lenght should be quadrupled
D. its length should be doubled.

109. For a particle moving with a simple harrmonic motion, the frequency is

A. directly proportional to periodic time
B. inversely proportional to periodic time
C. inversely proportional to its angular velocity
D. directly proportional to its angular velocity
E. none of these.

110. Energy may be defined as

A. power of doing work
B. capacity of doing work
C. rate of doing work
D. all the above.

111. The intrinsic equation of catenary is

A. S = c tan ψ
B. y = c cosh x/c
C. y = c cosh ψ
D. y = c sinh ψ.

112. A ball which is thrown upwards, returns to the ground describing a parabolic path during its flight

A. vertical component of velocity remains constant
B. horizontal component of velocity remains constant
C. speed of the ball remains constant
D. kinetic energy of the ball remains constant.

113. A stone is whirled in a vertical circle, the tension in the string, is maximum

A. when the string is horizontal
B. when the stone is at the highest position
C. when the stone is at the lowest position
D. at all the positions.

114. If a spherical body is symmetrical about its perpendicular axes, the moment of inertia of the body about an axis passing through its centre of gravity as given by Routh’s rule is obtained by dividing the product of the mass and the sum of the squares of two semi-axes by n where n is

A. 2
B. 3
C. 4
D. 5.

115. The angle of projection for a range is equal to the distance through which the particle would have fallen in order to acquire a velocity equal to the velocity of projection, will be

A. 30°
B. 45°
C. 60°
D. 75°.

116. A particle executes a simple harmonic motion. While passing through the mean position, the particle possesses

A. maximum kinetic energy and minimum potential energy
B. maximum kinetic energy and maximum potential energy
C. minimum kinetic energy and maximum potential energy
D. minimum kinetic, energy and minimum potential energy
E. none of these.

117. Varigon’s theorem of moments states

A. arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
B. algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
C. arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
D. algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resulant about that point.

118. A smooth cylinder lying on its convex surface remains

A. in stable equilibrium
B. in unstable equilibrium
C. in neutral equilibrium
D. out of equilibrium
E. none of these.

119. A weight W is suspended at the free end of a light member hinged to a vertical wall. If the angle of inclination of the member with the upper wall is θ°, the force introduced in the member, is

A. W sec θ
B. W cos θ
C. W sin θ
D. W cosec θ
E. W tan θ.

120. A satellite goes on moving along its orbit round the earth due to

A. gravitational force
B. centrifugal force
C. centripital force
D. none of these.

121. The phenomenon of collision of two elastic bodies takes place because bodies

A. immediately after collision come momentarily to rest
B. tend to compress each other till they are compressed maximum possible
C. attempt to regain its original shape due to their elasticities
D. all the above.

122. A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is

A. 0.25
B. 0.33
C. 0.40
D. 0.50
E. 0.55

123. Kinetic friction may be defined as

A. friction force acting when the body is just about to move
B. friction force acting when the body is in motion
C. angle between normal reaction and resultant of normal reaction and limiting friction
D. ratio of limiting friction and normal reaction.

124. The centre of gravity of a homogenous body is the point at which the whole

A. volume of the body is assumed to be concentrated
B. area of the surface of the body is assumed to be concentrated
C. weight of the body is assumed to be concentrated
D. all the above.

125. Pick up the correct statement from the following :

A. If two equal and perfectly elastic smooth spheres impinge directly, they interchange their velocities.
B. If a sphere impinges directly on an equal sphere which is at rest, then a fraction (1 – e2) the original kinetic energy is lost by the impact.
C. If a smooth sphere impinges on another sphere, which is at rest, the latter will move along the line of centres.
D. If two equal spheres which are perfectly elastic impinge at right angles, their direction after impact will still be at right angles.
E. All the above.

126. Centre of gravity of a thin hollow cone lies on the axis of symmmetry at a height of

A. one-half of the total height above base
B. one-third of the total height above base
C. one-fourth of the total height above base
D. none of these.

127. A ball of mass 1 kg moving with a velocity of 2 m/sec collides a stationary ball of mass 2 kg and comes to rest after impact. The velocity of the second ball after impact will be

A. zero
B. 0.5 m/sec
C. 1.0 m/sec
D. 2.0 m/sec.

128. Periodic time of a particle moving with simple harmonic motion is the time taken by the particle for

A. half oscillation
B. quarter oscillation
C. complete oscillation
D. none of these.

129. Pick up the correct statement from the following. The kinetic energy of a body

A. before impact is equal to that after impact
B. before impact is less than that after impact
C. before impact is more than that after impact
D. remains constant
E. none of these.

130. The motion of a bicycle wheel is

A. translatory
B. rotary
C. rotary and translatory
D. curvilinear

131. The practical units of work, is

A. erg
B. joule
C. Newton
D. dyne.

132. The Centre of gravity of a 10 x 15 x 5 cm T section from its bottom, is

A. 7.5 cm
B. 5.0 cm
C. 8.75 cm
D. 7.85 cm
E. none of above.

133. For a self-locking machine, the efficiency should be

A. less than 60%
B. 50%
C. more than 50%
D. None of these.

134. When a body moves round a fixed axis, it has

A. a rotary motion
B. a circular motion
C. a translatory
D. a rotary motion and translatory motion.

135. The rate of change of displacement of a body with respect to its surrounding, is known

A. velocity
B. acceleration
C. speed
D. none of these.

136. The C.G. of a hemisphere from its base measured along the vertical radius is at a distance of

A.
B.
C.
D.
E. R/2.

137. The rotational velocity of a satellite is increased by 450 m per second if its launch is done from equator

A. eastward
B. northward
C. westward
D. southward
E. upward.

138. From a solid cylinder of height 8 cm and radius 4 cm, a right circular cone is scooped out on the same base and having the same height as that of the cylinder. The c.g. of the remainder is at a height of

A. 4.5 cm
B. 5.0 cm
C. 5.25 cm
D. 5.5 cm.

139. When a body falls freely under gravitational force, it possesses

A. maximum weight
B. minimum weight
C. no weight
D. no effect on its weight.

140. A rigid body suspended Vertically at a point and oscillating with a small amplitude under the action of the force of gravity, is called

A. simple pendulum
B. compour pendulum
C. Second’s pendulum
D. none of these.

141. If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and floor, is

A. 0.25
B. 0.50
C. 0.67
D. 0.33
E. 0.75

142. The piston of a steam engine moves with a simple harmonic motion. The crank rotates 120 r.p.m. and the stroke length is 2 metres. The linear velocity of the piston when it is at a distance of 0.5 metre from the centre, is

A. 5.88 m/sec
B. 8.88 m/sec
C. 10.88 m/sec
D. 12.88 m/sec.

143. When a body slides down an inclined surface, the acceleration (f) of the body, is given by

A. f = g
B. f = g sin θ
C. f = g cos θ
D. f = g tan θ.

144. The velocity ratio of an inclined plane of inclination θ with horizontal for lifting a load is

A. sin θ
B. cos θ
C. tan θ
D. sec θ
E. cosec θ.

145. The frequency of oscillation on moon as compared to that on earth, will be

A. 2.44 times more
B. 2.44 times less
C. 3 times less
D. 3 times more.

146. Pick up the incorrect statement from the following. In a simple harmonic motion

A. velocity is maximum at its mean position
B. velocity is minimum at the end of the storke
C. acceleration is minimum at the end of the stroke
D. acceleration is zero at the mean position.

147. The gravitational force makes a satellite go round the earth in a circular orbit, if it is projected with an initial velocity of

A. 8.04 km/sec at a height of 285 km
B. 11.11 km/sec at a height of 37, 400 km
C. 11.26 km/sec, the satellite escapes the pull of the earth
D. all the above.

148. The point about which combined motion of rotation and translation of a rigid body takes place, is known as

A. Virtual centre
B. Instantaneous centre
C. Instantaneous axis
D. Point of rotation
E. All the above.

149. A particle is dropped from the top of a tower 60 m high and another is projected upwards from the foot of the tower to meet the first particle at a height of 15.9 m. The velocity of projection of the second particle is

A. 16 m/sec
B. 18 m/sec
C. 20 m/sec
D. 22 m/sec.

150. A point subjected to a number of forces will be in equilibrium, if

A. sum of resolved parts in any two directions at right angles, are both zero
B. algebraic sum of the forces is zero
C. two resolved parts in any two directions at right angles are equal
D. algebraic sum of the moments of the forces about the point is zero
E. none of these.

151. Periodic time of body moving with simple harmonic motion, is

A. directly proportional to its angular velocity
B. directly porportional to the square of its angular velocity
C. inversly proportional to the square of its angular velocity
D. inversely proportional to its angular velocity.

152. On a ladder resting on a rough ground and leaning against a smooth vertical wall, the force of friction acts

A. downwards at its upper end
B. upwards at its upper end
C. perpendicular to the wall at its upper end
D. zero at its upper end
E. none of these.

153. The centre of gravity of a plane lamina will not be at its geometrical centre if it is a

A. circle
B. equilateral triangle
C. rectangle
D. square
E. right angled triangle.

154. The motion of a particle moving with S.H.M. from an extremity to the other, constitutes

A. half an oscillation
B. one full oscillation
C. two oscillations
D. none of these.

155. Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by

A. 5.5 kg
B. 6.25 kg
C. 8.75 kg
D. 10.5 kg.

156. The velocity of a moving body, is

A. a vector quantity
B. a scalar quantity
C. a constant quantity
D. none of these.