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
2. If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is
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
4. The angles between two forces to make their resultant a minimum and a maximum respectively are
5. When two forces, each equal to P, act at 90° to each other, then the resultant will be
6. The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
7. A cube on a smooth horizontal surface
8. The following is in unstable equilibrium
9. 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 ?
10. A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable ?
11. Minimum potential energy of a system will be in the position of
12. A rigid body is in a stable equilibrium if the application of any force
13. Which of the following represents the state of neutral equilibrium ?
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 ?
15. 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
16. 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
17. The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is
18. The torque produced by a force depends on
19. The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
20. 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 ?
21. A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its center of mass has a speed of 200 mm/sec, . The work required to stop the hoop is
22. 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
23. A solid sphere of mass M and radius R rolls down a plane inclined at 0 with the horizontal. The acceleration of sphere is
24. A cylinder will slip on an inclined plane of inclination 0 if the coefficient of static friction between plane and cylinder is
25. Rate of change of angular momentum is equal to
26. If the angular distance, 0 = 2t3 - 3t2, the angular acceleration at t = 1 sec. is
27. 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
28. 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
29. 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
30. 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
31. When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are
32. Select the correct statement
33. At the instantaneous center, the velocity of the moving lamina at any instant is
34. Instantaneous center is at infinity when the angular velocity is
35. A 2 m long ladder rests against a wall and makes an angle of 30° with the horizontal floor. Where will be the instantaneous center of rotation when the ladder starts slipping ?
36. For a given velocity of a projectile, the range is maximum when the angle of projection is
37. The angle of projection at which the horizontal range and maximum height of a projectile are equal to
38. The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is
39. A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in
40. 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
41. 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
42. 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
43. The angle of projection at which the horizontal range and maximum height of a projectile are equal to
44. 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 ?
45. In a simple harmonic motion, the position of equilibrium is always
46. If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is
47. The time period of a simple pendulum depends on
48. 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
50. The maximum displacement of a particle executing S.H.M. corresponds to
51. 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
52. 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
53. 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
54. The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
55. 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
56. Time period and length of a seconds pendulum respectively are
57. 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
58. 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
59. The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to
60. Joule is the unit of
61. One Newton is equivalent to
62. A quantity whose dimensions are M2L2 T3 could be the product of
63. The dimensions of Gravitational Universal constant 'G' are
64. If y is force and x is velocity, then dimensions of —=r are dx2
65. One Joule is equivalent to
66. The dimensions of centrifugal force are
67. 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 ?
68. The unit of rotational inertia of a body in C.G.S system is
69. The ratio of unit of force in gravitational system to that in absolute system is
70. In SI units, the units of force and energy are respectively
71. The dimensions of power are.
72. Impulse can be obtained from a
73. One Newton is equivalent to
74. Which of the following is a scalar quantity?
75. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
76. Coefficient of friction depends on
77. 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
78. 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 incli¬nation 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
79. If a body is lying on a plane whose in-clination with the horizontal is less than the angle of friction, then
80. Intrinisic equation of catenary is given by
81. The shape of a suspended cable for a uniformly distributed load over it is
82. Cartesian form of the equation of catenary is
83. 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
84. Minimum pull in a suspended cable with supports at two ends is equal to
85. A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
86. The maximum pull in a cable, carrying a uniformly distributed load and supported at two ends which are at the same level, is at
87. 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
88. 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
89. 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
90. 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 centres. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
91. When a body slides down an inclined surface, the acceleration of the body is given by
92. 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
93. 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
94. 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)
95. 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
96. If a flywheel increases its speed from 10 rpm to 20 rpm in 10 seconds, then its angular acceleration is
97. 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
98. The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
99. A bullet weighing 10 gm moves with a velocity of lkm/sec. Its kinetic energy is
100. 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)