Real Time Applied Mechanics Online Quiz Questions and Answers
1. 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
Ans: d
2. 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°
Ans: d
3. A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
a) 109.5 mm from A
b) 119.5 mm from A
c) 125.5 mm from A
d) 132.5 mm from A
Ans: a
4. 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°
Ans: d
5. 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
Ans: b
6. 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
Ans: b
12. 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
Ans: d
13. 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
Ans: c
14. 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
Ans: b
15. 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
Ans: a
16. 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
Ans: a
17. 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 the above
Ans: a
18. 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
Ans: d
25. 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
Ans: b
31. 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
Ans: c
32. 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
Ans: c
33. The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is
a) 0.1 radian/sec
b) 1 radian/sec
c) 100 radian/sec
d) 1000 radian/sec
Ans: a
34. The torque produced by a force depends on
i) the magnitude of the force
ii) the direction of the force
iii) the'point of application of the force relative to origin The correct answer is
a) only (i)
b) both (i) and (ii)
c) both (i) and (iii)
d) all (i), (ii) and (iii)
Ans: d
35. 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
Ans: a
36. 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
Ans: b
38. 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
Ans: b
39. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The acceleration of centre 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
where 'g' is acceleration due to gravity and 0 is inclination of plane with hori¬zontal.
Ans: c
40. 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
where g is acceleration due to gravity
Ans: d
41. 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
Ans: a
42. Rate of change of angular momentum is equal to
a) force
b) torque
c) linear momentum
d) impulse
Ans: b
43. If the angular distance, 0 = 2t3 - 3t2, the angular acceleration at t = 1 sec. is
a) 1 rad/sec2
b) 4 rad/sec2
c) 6 rad/sec2
d) 12 rad/sec2
Ans: c
44. 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
Ans: b
45. 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 metres. The maximum velocity during the motion is
a) 6 m/sec
b) 12 m/sec
c) 24 m/sec
d) 48 m/sec
Ans: b
46. 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
Ans: b
47. A disc of mass 4 kg, radius 0.5m and moment of inertia 3 kg-m2 rolls on a horizontal surface so that its centre moves with speed 5 m/see. Kinetic energy of the disc is
a) 50 J
b) 150 J
c) 200 J
d) 400 J
Ans: c
48. 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
Ans: c
49. 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.
Ans: a
50. At the instantaneous centre, the velocity of the moving lamina at any instant is
a) zero
b) maximum
c) minimum
d) varying
Ans: a
51. Instantaneous centre is at infinity when the angular velocity is
a) constant
b) zero
c) maximum
d) minimum
Ans: b
53. A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous centre of rotation when the ladder starts slipping ?
i) 1.0 in from the wall
ii) 1.732 m from the wall
iii) 1.0 m above the floor
iv) 1.732 m above the floor The correct answer is
a) (i) and (iii)
b) (i) and (iv)
c) (ii) and (iii)
d) (ii) and (iv)
Ans: d
54. 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°
Ans: b
55. 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°
Ans: d
56. 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) 1960m
Ans: c
57. 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
Ans: c
58. 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
Assume g = 10 m/sec2
Ans: a
60. 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
Ans: b
61. 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
Ans: b
62. 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)
Ans: c
64. 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°
Ans: a
66. In a simple harmonic motion, the position of equilibrium is always
a) stable
b) unstable
c) neutral
d) none of the above
Ans: a
67. 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
Ans: b
68. The time period of a simple pendulum depends on
i) mass of suspended particle
ii) length of the pendulum
iii) acceleration due to gravity The correct answer is
a) only (i)
b) both (ii) and (iii)
c) both (i) and (iii)
d) all are correct
Ans: b
69. 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
Ans: b
70. 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
Ans: b
71. 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
Ans: d
72. 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
Ans: d
73. 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
Ans: c
74. 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
Ans: d
75. 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
Ans: b
76. 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
Ans: c
77. 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
Ans: a
78. 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
Ans: c
79. 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
where r is the distance of'the particle from centre of the earth
Ans: c
80. Joule is the unit of
a) power
b) impulse
c) work
d) momentum
Ans: c
81. One Newton is equivalent to
a) 105 dyne
b) 106 dyne.
c) 107 dyne
d) 981 dyne
Ans: a
82. 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
Ans: b
83. The dimensions of Gravitational Universal constant 'G' are
a) M-'L2r2
b) M-'L3r2
c) M-2L3T2
d) M'L3T2
Ans: b
84. 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
Ans: b
85. One Joule is equivalent to
a) 9.81 Newton - metre
b) 1 Newton - metre
c) 1 kg wt - metre
d) 1 dyne - metre
Ans: b
86. The dimensions of centrifugal force are
a) M1 L2 T2
b) M'L'T1
c) M'L'T2
d) M'L-'T2
Ans: c
87. A quantity measured in the C.G.S system of units has dimensions M"2L3 T3/2. What numerical factor would be required to convert the quantity to SI units ?
a) 1
b) 100
c) 1/100
d) 1/10000
Ans: a
88. 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
Ans: c
89. The ratio of unit of force in gravitational system to that in absolute system is
a) 1
b) g
c) 1/g
d) none of the above
where 'g' is acceleration due to gravity
Ans: b
91. 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
Ans: c
92. The dimensions of power are.
a) M'L2T2
b) M'L'T3
c) M'L'r2
d) M'L-'T*
Ans: b
93. Impulse can be obtained from a
a) force-displacement diagram
b) force-time diagram
c) velocity-time diagram
d) velocity-displacement diagram
Ans: b
94. One Newton is equivalent to
a) 1 kg-wt
b) 9.81 kg-wt
c) 981 dyne
d) 1/9.81 kg-wt
Ans: d
95. Which of the following is a scalar quantity?
a) energy
b) momentum
c) torque
d) impulse
Ans: a
97. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
a) floor is smooth and wall is rough
b) floor is rough and wall is rough
c) both floor and wall are rough
d) both floor and wall are smooth
Ans: d
98. 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
Ans: a
100. A rope is wrapped twice around a rough pole with a coefficient of friction 'A . It is subjected to a force Fj at one end and a gradually increasing force F2 is applied at the other end till the rope just starts slip-ping. At this instant the ratio of F2 to Fi is
a) 1
b) e2*
c) e4*
d) e*72
Ans: b
b) 80 N
c) 100 N
d) 120 N
Ans: d
2. 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°
Ans: d
3. A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
a) 109.5 mm from A
b) 119.5 mm from A
c) 125.5 mm from A
d) 132.5 mm from A
Ans: a
4. 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°
Ans: d
5. 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
Ans: b
6. 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
Ans: b
12. 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
Ans: d
13. 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
Ans: c
14. 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
Ans: b
15. 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
Ans: a
16. 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
Ans: a
17. 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 the above
Ans: a
18. 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
Ans: d
25. 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
Ans: b
31. 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
Ans: c
32. 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
Ans: c
33. The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is
a) 0.1 radian/sec
b) 1 radian/sec
c) 100 radian/sec
d) 1000 radian/sec
Ans: a
34. The torque produced by a force depends on
i) the magnitude of the force
ii) the direction of the force
iii) the'point of application of the force relative to origin The correct answer is
a) only (i)
b) both (i) and (ii)
c) both (i) and (iii)
d) all (i), (ii) and (iii)
Ans: d
35. 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
Ans: a
36. 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
Ans: b
38. 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
Ans: b
39. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The acceleration of centre 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
where 'g' is acceleration due to gravity and 0 is inclination of plane with hori¬zontal.
Ans: c
40. 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
where g is acceleration due to gravity
Ans: d
41. 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
Ans: a
42. Rate of change of angular momentum is equal to
a) force
b) torque
c) linear momentum
d) impulse
Ans: b
43. If the angular distance, 0 = 2t3 - 3t2, the angular acceleration at t = 1 sec. is
a) 1 rad/sec2
b) 4 rad/sec2
c) 6 rad/sec2
d) 12 rad/sec2
Ans: c
44. 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
Ans: b
45. 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 metres. The maximum velocity during the motion is
a) 6 m/sec
b) 12 m/sec
c) 24 m/sec
d) 48 m/sec
Ans: b
46. 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
Ans: b
47. A disc of mass 4 kg, radius 0.5m and moment of inertia 3 kg-m2 rolls on a horizontal surface so that its centre moves with speed 5 m/see. Kinetic energy of the disc is
a) 50 J
b) 150 J
c) 200 J
d) 400 J
Ans: c
48. 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
Ans: c
49. 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.
Ans: a
50. At the instantaneous centre, the velocity of the moving lamina at any instant is
a) zero
b) maximum
c) minimum
d) varying
Ans: a
51. Instantaneous centre is at infinity when the angular velocity is
a) constant
b) zero
c) maximum
d) minimum
Ans: b
53. A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous centre of rotation when the ladder starts slipping ?
i) 1.0 in from the wall
ii) 1.732 m from the wall
iii) 1.0 m above the floor
iv) 1.732 m above the floor The correct answer is
a) (i) and (iii)
b) (i) and (iv)
c) (ii) and (iii)
d) (ii) and (iv)
Ans: d
54. 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°
Ans: b
55. 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°
Ans: d
56. 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) 1960m
Ans: c
57. 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
Ans: c
58. 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
Assume g = 10 m/sec2
Ans: a
60. 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
Ans: b
61. 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
Ans: b
62. 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)
Ans: c
64. 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°
Ans: a
66. In a simple harmonic motion, the position of equilibrium is always
a) stable
b) unstable
c) neutral
d) none of the above
Ans: a
67. 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
Ans: b
68. The time period of a simple pendulum depends on
i) mass of suspended particle
ii) length of the pendulum
iii) acceleration due to gravity The correct answer is
a) only (i)
b) both (ii) and (iii)
c) both (i) and (iii)
d) all are correct
Ans: b
69. 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
Ans: b
70. 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
Ans: b
71. 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
Ans: d
72. 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
Ans: d
73. 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
Ans: c
74. 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
Ans: d
75. 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
Ans: b
76. 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
Ans: c
77. 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
Ans: a
78. 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
Ans: c
79. 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
where r is the distance of'the particle from centre of the earth
Ans: c
80. Joule is the unit of
a) power
b) impulse
c) work
d) momentum
Ans: c
81. One Newton is equivalent to
a) 105 dyne
b) 106 dyne.
c) 107 dyne
d) 981 dyne
Ans: a
82. 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
Ans: b
83. The dimensions of Gravitational Universal constant 'G' are
a) M-'L2r2
b) M-'L3r2
c) M-2L3T2
d) M'L3T2
Ans: b
84. 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
Ans: b
85. One Joule is equivalent to
a) 9.81 Newton - metre
b) 1 Newton - metre
c) 1 kg wt - metre
d) 1 dyne - metre
Ans: b
86. The dimensions of centrifugal force are
a) M1 L2 T2
b) M'L'T1
c) M'L'T2
d) M'L-'T2
Ans: c
87. A quantity measured in the C.G.S system of units has dimensions M"2L3 T3/2. What numerical factor would be required to convert the quantity to SI units ?
a) 1
b) 100
c) 1/100
d) 1/10000
Ans: a
88. 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
Ans: c
89. The ratio of unit of force in gravitational system to that in absolute system is
a) 1
b) g
c) 1/g
d) none of the above
where 'g' is acceleration due to gravity
Ans: b
91. 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
Ans: c
92. The dimensions of power are.
a) M'L2T2
b) M'L'T3
c) M'L'r2
d) M'L-'T*
Ans: b
93. Impulse can be obtained from a
a) force-displacement diagram
b) force-time diagram
c) velocity-time diagram
d) velocity-displacement diagram
Ans: b
94. One Newton is equivalent to
a) 1 kg-wt
b) 9.81 kg-wt
c) 981 dyne
d) 1/9.81 kg-wt
Ans: d
95. Which of the following is a scalar quantity?
a) energy
b) momentum
c) torque
d) impulse
Ans: a
97. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
a) floor is smooth and wall is rough
b) floor is rough and wall is rough
c) both floor and wall are rough
d) both floor and wall are smooth
Ans: d
98. 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
Ans: a
100. A rope is wrapped twice around a rough pole with a coefficient of friction 'A . It is subjected to a force Fj at one end and a gradually increasing force F2 is applied at the other end till the rope just starts slip-ping. At this instant the ratio of F2 to Fi is
a) 1
b) e2*
c) e4*
d) e*72
Ans: b
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