# Applied Mechanics and Graphics Statics MCQs

1. In a forced vortex, the velocity of flow everywhere within the fluid is__________________?.

A. maximum
B. minimum
C. zero
D. non-zero finite

2. Select the correct statement ?.
A. Local atmospheric pressure depends upon elevation of locality only
B. Standard atmospheric pressure is the mean local atmospheric pressure a* sea level
C. Local atmospheric pressure is always below standard atmospheric pressure
D. A barometer reads the difference be-tween local and standard atmospheric pressure
Answer = Standard atmospheric pressure is the mean local atmospheric pressure a* sea level

3. Choose the wrong statement ?.
A. The center of buoyancy is located at the center of gravity of the displaced liquid
B. For stability of a submerged body, the center of gravity of body must lie directly below the center of buoyancy
C. If e.g. and center of buoyancy coincide, the submerged body must lie at neutral equilibrium for all positions
D. All floating bodies are stable.
Answer = All floating bodies are stable

4. Choose the wrong statement?.
A. any weight, floating or immersed in a liquid, is acted upon by a buoyant force
B. Buoyant force is equal to the weight of the liquid displaced
C. The point through which buoyant force acts, is called the center of buoyancy
D. Center of buoyancy is located above the center of gravity of the displaced liquid v
Answer = Center of buoyancy is located above the center of gravity of the displaced liquid v

5. Select the correct statement ?.
A. The body centrode rolls on the space centrode
B. The space centrode rolls on the body centrode
C. Both body and space centrodes may role on each other
D. The body centrode never touches space centrode.
Answer = The body centrode rolls on the space centrode

6. A force P of 50 N and another force Q of unknown magnitude act at 90° to each other. They are balanced by a force of 130 N. The magnitude of Q is__________________?.
A. 60 N
B. 80 N
C. 100 N
D. 120 N.

7. If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is____________________?.
A. 30°
B. 45°
C. 60°
D. 120°.

8. The angles between two forces to make their resultant a minimum and a maximum respectively are__________________?.
A. 0° and 90°
B. 180° and 90°
C. 90° and 180°
D. 180° and 0°.

9. The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then_________________?.
A. P = R
B. Q = R
C. P = Q
D. None of the above is correct.

10. A disc of mass 4 kg, radius 0.5m and moment of inertia 3 kg-m2 rolls on a horizontal surface so that its center moves with speed 5 m/see. Kinetic energy of the disc is ___________________?.
A. 50 J
B. 150 J
C. 200 J
D. 400 J.

11. The following is in unstable equilibrium__________________?.
A. a uniform solid cone resting on a generator on a smooth horizontal plane
B. a uniform solid cone resting on its base on a horizontal plane
C. a solid cube resting on one edge
D. a satellite encircling the earth.
Answer = a solid cube resting on one edge

12. A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable ?.
A. pyramid
B. prism
C. both equally stable
D. none of the above.

13. A rigid body is in a stable equilibrium if the application of any force__________________?.
A. can raise the CG of the body but can not lower it
B. tends to lower the CG of the body
C. neither raises nor lowers the CG of the body
D. none of above.
Answer = can raise the CG of the body but can not lower it

14. Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis ?.
A. disc with larger density
B. disc with smaller density
C. both discs will have same rotational inertia
D. none of the above.
Answer = disc with smaller density

15. A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 2 kg -m2 and its rate of rotation 2 revolutions/see. The angular momentum of the body in kg-m2/sec is_____________________?.
A. 4
B. 6 7i
C. 8TC
D. 8.

16. A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first ?.
A. sphere with greater rotational energy at bottom than cylinder
B. sphere with lesser rotational energy at bottom than cylinder
C. cylinder with greater rotational energy at bottom than sphere
D. both reach the bottom simultaneously with equal rotational energy at bottom.
Answer = sphere with lesser rotational energy at bottom than cylinder

17. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The acceleration of center of mass of rolling cylinder is________________?.
A. (1/3) g sinB
B. (2/3) g cos 9
C. (2/3) g sin 0
D. g sin 9.
Answer = (2/3) g sin 0

18. A cylinder will slip on an inclined plane of inclination 0 if the coefficient of static friction between plane and cylinder is_____________________?.
A. less than (1/3) tan 0
B. less than (2/3) tan 0
C. less than (1/3) sin 6
D. less than (2/3) sin 6.
Answer = less than (1/3) tan 0

19. If the angular distance, 0 = 2t3 – 3t2, the angular acceleration at t = 1 sec. is__________________?.

20. A particle moves in a straight line and its position is defined by the equation x = 6 t2 – t3 where t is expressed in seconds and x in meters. The maximum velocity during the motion is_________________?.
A. 6 m/sec
B. 12 m/sec
C. 24 m/sec
D. 48 m/sec.

21. Instantaneous center is at infinity when the angular velocity is _________________?.
A. constant
B. zero
C. maximum
D. minimum.

22. The angle of projection at which the horizontal range and maximum height of a projectile are equal to_____________________?.
A. 36°
B. 45°
C. 56°
D. 76°.

23. A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in________________?.
A. 5 sec
B. 8 sec
C. 10 sec
D. 20 sec.

24. If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is__________________?.
A. zero
B. maximum
C. minimum
D. unpredictable.

25. The angle of projection at which the horizontal range and maximum height of a projectile are equal to___________________?.
A. 45°
B. tan-1 (2)
C. tan-' (4)
D. tan”1 (1/4).

26. In a simple harmonic motion, the position of equilibrium is always_________________?.
A. stable
B. unstable
C. neutral
D. none of the above.

27. The maximum displacement of a particle executing S.H.M. corresponds to__________________?.
A. zero potential energy and maximum kinetic energy
B. zero kinetic energy and maximum potential energy
C. maximum kinetic energy and maxi-mum potential energy
D. minimum kinetic energy and minimum potential energy.
Answer = zero kinetic energy and maximum potential energy

28. A simple pendulum of length 1 has an energy E when its amplitude is A. If its amplitude is increased to 2 A, the energy becomes____________________?.
A. E
B. E/2
C. 2E
D. 4E.

29. The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by__________________?.
A. 1:2
B. 1:1
C. 2:1
D. 3:1.

30. Time period and length of a seconds pendulum respectively are_________________?.
A. 1 sec and 99.4 cm
B. 1 sec and 92.7 cm
C. 2 sec and 99.4 cm
D. 2 sec and 92.7 cm.
Answer = 2 sec and 99.4 cm

31. A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is___________________?.
A. 1.00 m/sec
B. 1.57 m/sec
C. 3.14 m/sec
D. 6.28 m/sec.

32. Joule is the unit of__________________?.
A. power
B. impulse
C. work
D. momentum.

33. A quantity whose dimensions are M2L2 T3 could be the product of_________________?.
A. force and pressure
B. mass and power
C. energy and velocity
D. force and velocity.

34. If y is force and x is velocity, then dimensions of —=r are dx2__________________?.
A. M'^T'
B. M'L-'T0
C. M'L-'T1
D. M2L'T3.

35. The dimensions of centrifugal force are__________________?.
A. M1 L2 T2
B. M'L'T1
C. M'L'T2
D. M'L-'T2.

36. The unit of rotational inertia of a body in C.G.S system is________________?.
A. cm4
B. kg-cm2
C. gm-cm2
D. gm-cm3.

37. In SI units, the units of force and energy are respectively___________________?.
A. Newton and watt
B. Dyne and erg
C. Newton and joule
D. kg-wt and joule.

38. A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are____________________?.
A. 1346.3 kN and 1500 kN
B. 1436.2 kN and 1250 kN
C. 1346.3 kN and 1250 kN
D. 1436.2 kN and 1500 kN.
Answer = 1346.3 kN and 1250 kN

39. Impulse can be obtained from a_________________?.
A. force-displacement diagram
B. force-time diagram
C. velocity-time diagram
D. velocity-displacement diagram.

40. Which of the following is a scalar quantity ?.
A. energy
B. momentum
C. torque
D. impulse.

41. Coefficient of friction depends on__________________?.
A. nature of surfaces only
B. area of contact only
C. both (A) and (B)
D. none of the above.
Answer = nature of surfaces only

42. A ladder of weight 'w' rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of inclination of the ladder to the vertical, if a man of weight 'w' is to walk to the top of it safely, is tan'1 x, where x is___________________?.
A. 1/4
B. 1/3
C. 3
D. 4.

43. The shape of a suspended cable for a uniformly distributed load over it is__________________?.
A. circular
B. parabolic
C. catenary
D. cubic parabola.

44. A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a_____________________?.
A. parabola
B. catenary
C. cycloid
D. ellipse.

45. A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is___________________?.
A. 1/3
B. 2/3
C. 1/9
D. 8/9.

46. A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is_____________________?.
A. 1/4
B. 2/3
C. 3/4
D. 4/3.

47. When a body slides down an inclined surface, the acceleration of the body is given by__________________?.
A. g
B. gsinG
C. g cos 6
D. g tan 6.

48. A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan”1 x, where x is______________________?.
A. 3/4
B. 4/5
C. 5/3
D. 3/5.

49. A shell of mass 100 kg travelling with a velocity of 10 m/sec breaks into two equal pieces during an explosion which provides an extra kinetic energy of 20000 Joules. If the pieces continue to move in the same direction as before, then the speed of the faster one must be____________________?.
A. 20 m/sec
B. 30 m/sec
C. 40 m/sec
D. 50 m/sec.

50. Two objects moving with uniform speeds are 5 m apart after 1 second when they move towards each other and are 1 m apart when they move in the same direction. The speeds of the objects are____________________?.
A. 2 m/sec and 2 m/sec
B. 3 m/sec and 2 m/sec
C. 3 m/sec and 3 m/sec
D. 4 m/sec and 6 m/sec.
Answer = 3 m/sec and 2 m/sec

51. The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be___________________?.

52. The condilion for a lifting machine to be reversible is that its efficiency should be_________________?.
A. less than 50%
B. more than 50%
C. more than 66.67%
D. equal to 100%.

53. In a lifting machine with efficiency 60%, an effort of 200 N is required to raise a load of 6 kN. The velocity ratio of the machine is_____________________?.
A. 30
B. 50
C. 60
D. 80.

54. A system of copianar forces acting on a rigid body can be reduced to________________?.
A. one force only
B. one couple only
C. one force and one couple only
D. none of the above.
Answer = one force and one couple only

55. Force polygon method is applicable for_____________________?.
A. any copianar force system
B. a system of parallel forces only
C. concurrent copianar force system
D. non-concurrent copianar force system.
Answer = concurrent copianar force system

56. The diagram showing the point of application and line of action of forces in their plane is called____________________?.
A. vector diagram
B. space diagram
C. force diagram
D. funicular diagram.

57. The bending moment in an arch is proportional to___________________?.
A. vertical ordinate of funicular polygon
B. vertical ordinate of the arch
C. intercept between the arch axis and the funicular polygon
D. none of these.
Answer = intercept between the arch axis and the funicular polygon

58. An ordinate in a funicular polygon represents__________________?.
A. shear force
B. resultant force
C. bending moment
D. equilibrium.

59. In which of the following trusses, the method of substitution is required for determining the forces in all the members of the truss by graphic statics ?.
A. howe truss
B. king post truss
C. fink truss
D. warren truss.

60. The number of funicular polygons which can be drawn to pass through two specified points in the space diagram are__________________?.
A. zero
B. 1
C. 2
D. infinity.

61. If the given forces P,, P2, P3 and P4 are such that the force polygon does not close, then the system will___________________?.
A. be in equilibrium
B. always reduce to a resultant force
C. always reduce to a couple
D. both (A) and (C).
Answer = always reduce to a resultant force

62. Williot-Mohr diagram is used to determine deflection in__________________?.
A. trusses only
B. beam only
C. rigid frames only
D. any type of structure.

63. For a non-concurrent force system to be in equilibrium__________________?.
A. only the closure of force polygon is sufficient
B. only the closure of funicular polygon is sufficient
C. both force polygon and funicular polygon must close
D. none of the above.
Answer = both force polygon and funicular polygon must close

64. The condition of equilibrium for any system of forces in a plane is____________________?.
A. that polygon of forces must close
B. that resultant couple must be zero
C. both (A) and (B)
D. none of the above.
Answer = both (A) and (B)

65. A funicular polygon cannot be made to pass through___________________?.
A. one specified point
B. two specified points
C. three specified points
D. more than three specified points.
Answer = more than three specified points

66. The pole distance is measured in___________________?.
A. distance scale
B. force scale
C. mass scale
D. time scale.

67. The member forces in a statically in determinate truss____________________?.
A. can be obtained by graphic statics
B. cannot be obtained by graphic statics
C. may be obtained by graphic statics
D. can be obtained by graphic statics by trial and error.
Answer = cannot be obtained by graphic statics

68. The graphical method of determining the forces in the members of a truss is based on________________?.
A. method of joint
B. method of section
C. either method
D. none of the two methods.

69. The force polygon representing a set of forces in equilibrium is a_____________________?.
A. triangle
B. open polygon
C. closed polygon
D. parallelogram.

70. A system of copianar forces is in equilibrium when___________________?.
A. force polygon closes
B. funicular polygon closes
C. both force polygon” and funicular polygon close
D. all the forces are concurrent.
Answer = both force polygon” and funicular polygon close

71. Free body diagram is an____________________?.
A. isolated joint with only body forces acting on it
B. isolated joint with internal forces acting on it
C. isolated joint with all the forces, internal as well as external, acting on it
D. none of the above.
Answer = isolated joint with all the forces, internal as well as external, acting on it

72. In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively_____________________?.
A. 50 and 75
B. 75 and 50
C. 75 and 75
D. 50 and 50.

73. A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec2)______________________?.
A. 15 m/sec
B. 25 m/sec
C. 40 m/sec
D. 50 m/sec.

74. A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is____________________?.
A. 0.5 m
B. 0.75 m
C. 1.0 m
D. 1.5 m.

75. One Joule is equivalent to________________?.
A. 9.81 Newton – metre
B. 1 Newton – metre
C. 1 kg wt – metre
D. 1 dyne – metre.
Answer = 1 Newton – metre

76. If a flywheel increases its speed from 10 rpm to 20 rpm in 10 seconds, then its angular acceleration is_____________________?.
D. none of the above.

77. A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan”1 x, where x is (Assume g = 10 m/sec2)_____________________?.
A. 3/8
B. 1/2
C. 9/5
D. 5/8.

78. A body is dropped from a height of 100 m and at the same time another body is projected vertically upward with a velocity of 10 m/sec. The two particles will____________________?.
A. never meet
B. meet after 1 sec
C. meet after 5 sec
D. meet after 10 sec.
Answer = meet after 10 sec

79. Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centers. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is____________________?.
A. 2/3
B. 1/5
C. 3/5
D. 1/3.

80. The maximum pull in a cable, carrying a uniformly distributed load and supported at two ends which are at the same level, is at_____________________?.
A. supports
B. quarter span
C. mid span
D. none of the above.

81. One Newton is equivalent to_________________?.
A. 105 dyne
B. 106 dyne
C. 107 dyne
D. 981 dyne.

82. The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to____________________?.
A. log r
B. r
C. r2
D. 1/r.

83. At the instantaneous center, the velocity of the moving lamina at any instant is_________________?.
A. zero
B. maximum
C. minimum
D. varying.

84. Which of the following represents the state of neutral equilibrium ?.
A. a cube resting on one edge
B. a smooth cylinder lying on a curved surface
C. a smooth cylinder lying on a convex surface
D. none of the above.
Answer = none of the above

85. One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is___________________?.
A. a simple harmonic motion
B. a rectilinear motion with constant speed
C. a damped oscillatory motion
D. none of the above.
Answer = a simple harmonic motion

86. A simple pendulum of length / has an energy E, when its amplitude is A. If the length of pendulum is doubled, the energy will be___________________?.
A. E
B. E/2
C. 2E
D. 4E.

87. If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to_________________?.
A. A
B. A/2
C. A/V2
D. AV2.

88. It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to_________________?.
A. f
B. 1/f
C. 1/f2
D. f2.

89. A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is___________________?.
A. 4.5 J
B. 9.0 J
C. 12.0 J
D. 18.0 J.

90. If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is___________________?.
A. proportional to A
B. proportional to A2
C. proportional to 1/A2
D. independent of A.

91. A stone is thrown up a slope of inclination 60° to the horizontal. At what angle to the slope must the stone be thrown so as to land as far as possible from the point of projection ?.
A. 15°
B. 30°
C. 45°
D. 75°.

92. If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60° to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are___________________?.
A. 0 and 5 m/sec
B. 5 m/sec and 0
C. 5 V3 m/sec and 0
D. 5 and 5V3 m/sec.
Answer = 5 m/sec and 0

93. A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about__________________?.
A. 1/4
B. 1/3
C. 1/2
D. 1/5.

94. The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is__________________?.
A. 98 m
B. 490 m
C. 980 m
D. 1960 m.

95. For a given velocity of a projectile, the range is maximum when the angle of projection is___________________?.
A. 30°
B. 45°
C. 90°
D. 0°.

96. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are________________?.
A. straight line and parabola
B. straight line and circle
C. circle and straight line
D. circle and parabola.
Answer = circle and straight line

97. The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is_______________?.

98. The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is_______________?.
A. less than 1
B. equal to 1
C. between 1 and 2
D. greater than 2.

99. A flywheel of moment of inertia 20 kg-m” is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian persecond is__________________?.
A. 1/2
B. 3/2
C. 2
D. 3.

100. A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is___________________?.
A. n rpm
B. n/2 rpm
C. n/4 rpm
D. 2n rpm.

101. Rate of change of angular momentum is equal to_______________?.
A. force
B. torque
C. linear momentum
D. impulse.

102. A solid sphere of mass M and radius R rolls down a plane inclined at 0 with the horizontal. The acceleration of sphere is_______________?.
A. (1/3) g sin0
B. (2/5) g sin 0
C. (3/7) g sin 0
D. (5/7) g sin0.

103. A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec,The work required to stop the hoop is______________?.
A. 2 J
B. 4 J
C. 6 J
D. 8 J.

104. The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is_________________?.
A. 64 J
B. 400 J
C. 464 J
D. 89 J.

105. Minimum potential energy of a system will be in the position of________________?.
A. stable equilibrium
B. unstable equilibrium
C. neutral equilibrium
D. all of the above.

106. A block in the shape of a parallelopiped of sides lm x 2m x 3m lies on the surface. Which of the faces gives maximum stable block ?.
A. 1 m x 2 m
B. 2 m x 3 m
C. 1 m x 3m
D. equally stable on all faces.
Answer = 2 m x 3 m

107. A cube on a smooth horizontal surface___________________?.
A. cannot be in stable equilibrium
B. cannot be in neutral equilibrium
C. cannot be in unstable equilibrium
D. can be in any of these states.
Answer = can be in any of these states

108. When two forces, each equal to P, act at 90° to each other, then the resultant will be_____________?.
A. P
B. PV2
C. P/V2
D. 2P.