AjneeshFlame Institute

122. A hollow cylinder and a solid cylinder having the same mass and same diameter are released from rest simultaneously from the top of an inclined plane. Which will reach the bottom first

(a) The solid cylinder (b) The hollow cylinder (c) Both will reach the bottom together (d) The greater density Ans. a (7)

126. A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is

(a) √(2gh) (b) √(4/3 gh) (c) √(3/4 gh) (d) √(4g/h) Ans. b (3)

124. A solid cylinder rolls down an inclined plane from a height h. At any moment the ratio of rotational kinetic energy to the total kinetic energy would be

(a) 1 : 2 (b) 1 : 3 (c) 2 : 3 (d) 1 : 1 Ans. b (4)

121. A solid sphere (mass 2 M) and a thin hollow spherical shell (mass M) both of the same size, roll down an inclined plane, then

(a) Solid sphere will reach the bottom first (b) Hollow spherical shell will reach the bottom first (c) Both will reach at the same time (d) None of these Ans. a (34)

119. Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the fig. If the wheel rotates just once, the work done will be about (diameter of the wheel = 0.05m)

(a) 0.062 J (b) 0.031 J (c) 0.015 J (d) 0.057 J Ans. b (31)

120. A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

(a) Solid sphere (b) hollow sphere (c) Ring (d) All same Ans. d (23)

117. A uniform thin rod of length l is suspended from one of its ends and is rotated at f rotations per second. The rotational kinetic energy of the rod will be

(a) 2/3π2f2ml2 (b) 4/3 f2ml2 (c) 4π2f2ml2 (d) Zero Ans. a (19)

116. If L, M and P are the angular momentum, mass and linear momentum of a particle respectively which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius R

(a) L2/2M (b) P2/2MR (c) L2/2MR2 (d) MP/2 Ans. c (10)

115. A fly wheel of moment of inertia I is rotating at n revolutions per sec. The work needed to double the frequency would be

(a) 2π2 In2 (b) 4π2 In2 (c) 6π2 In2 (d) 8π2 In2 Ans. c (34)

114. A wheel of radius r rolls without slipping with a speed v on a horizontal road. When it is at a point A on the road, a small jump of mud separates from the wheel at its highest point B and drops at point C on the road. The distance AC will be

(a) v√r/g (b) 2v√r/g (c) 4v√r/g (d) √3r/g Ans. c (18)

113. An engine develops 100 kW, when rotating at 1800 rpm. Torque required to deliver the power is

(a) 531 N–m (b) 570 N–m (c) 520 N–m (d) 551 N–m Ans. a (4)

110. If the rotational kinetic energy of a body is increased by 300% then the percentage increase in its angular momentum will be

(a) 600% (b) 150% (c) 100% (d) 1500% Ans. c (7)

A tangential force F is applied on a disc of radius R, due to which it deflects through an angle θ from its initial position. The work done by this force would be

(a) FR (b) Fθ (c) FR/θ (d) FRθ Ans. d (25)

108. If a body completes one revolution in Π sec then the moment of inertia would be

(a) Equal to rotational kinetic energy (b) Double of rotational kinetic energy (c) Half of rotational kinetic energy (d) Four times the rotational kinetic energy Ans. c (17)

107. Rotational kinetic energy of a given body about an axis is proportional to

(a) Time period (b) (Time period)2 (c) (Time period)–1 (d) (time period)–2 Ans. d (9)

106. A circular disc has a mass of 1 kg and radius 40 cm. It is rotating about an axis passing through its centre and perpendicular to its plane with a speed of 10 rev/s. The work done in joules in stopping it would be

(a) 4 (b) 47.5 (c) 79 (d) 158 Ans. d (17)

105. A solid sphere of mass 1 kg rolls on a table with linear speed 1 m/s. Its total kinetic energy is

(a) 1 J (b) 0.5 J (c) 0.7 J (d) 1.4 J Ans. c (5)

104. A symmetrical body of mass M and radius R is rolling without slipping on a horizontal surface with linear speed v. Then its angular speed is

(a) v/R (b) Continuously increasing (c) Dependent on mass (d) Independent of radius (R) Ans. a (62)

103. The ratio of kinetic energies of two spheres rolling with equal centre of mass velocities is 2 : 1. If their radii are in the ratio 2 : 1; then the ratio of their masses will be

(a) 2:1 (b) 1:8 (c) 1:7 (d) 2√2:1 Ans. a (12)

102. A disc of radius 1m and 4 kg mass rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of 10 cm/s Its rotational kinetic energy is

(a) 0.01 erg (b) 0.02 joule (c) 0.03 joule (d) 0.01 joule Ans. d (49)

101. The speed of rolling of a ring of mass M changes from V to 3V. What is the change in its kinetic energy

(a) 3MV2 (b) 4MV2 (c) 6 MV2 (d) 8MV2 Ans. d (381)

100. A solid sphere is moving on a horizontal plane. Ratio of its transitional Kinetic energy and rotational energy is

(a) 1/5 (b) 5/2 (c) 3/5 (d) 5/7 Ans. b (6)

99. Ratio of kinetic energy and rotational energy in the motion of a disc is

(a) 1 : 1 (b) 2 : 7 (c) 1 : 2 (d) 3 : 1 Ans. d (9)

98.

A body of moment of inertia of 3kg-m2 rotating with an angular speed of 2 rad/sec has the same kinetic energy as a mass of 12 kg moving with a speed of (a) 1 m/s (b) 2 m/s (c) 4 …

The moment of inertia of a body about a given axis is 2.4 kg–m2. To produce a rotational kinetic energy of 750 J, an angular acceleration of 5 rad/s2 must be applied about that axis for (a) 6 sec (b) …

90.

In a bicycle the radius of rear wheel is twice the radius of front wheel. If rF and rr are the radii, vF and vr are speeds of top most points of wheel, then (a) vr = 2 vF (b) vF = …

85.

A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and center of mass with velocity v . It collides elastically and head-on with an identical sphere B at rest. Neglect friction everywhere. After the collision, …

69.

If I1 is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass, and I2 is the moment of inertia of the ring formed by bending the rod, …

67.

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia …

97. A body is rolling without slipping on a horizontal plane. If the rotational energy of the body is 40% of the total kinetic energy, then the body might be

(a) Cylinder (b) Hollow sphere (c) Solid cylinder (d) Ring Ans. b (12)

96. A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

(a) 2/5 (b) 2/7 (c) 3/5 (d) 3/7 Ans. b (3)

95. A thin hollow cylinder open at both ends:

(i) Slides without rotating (ii) Rolls without slipping, with the same speed. The ratio of kinetic energy in the two cases is (a) 1 : 1 (b) 4 : 1 (c) 1 : 2 (d) 2 : 1 Ans. c …