AjneeshFlame Institute

127. Solid cylinders of radii

Solid cylinders of radii r1,r2,r3 and roll down an inclined plane from the same place simultaneously. If , r1>r2>r3 which one would reach the bottom first (a) Cylinder of radius (b) Cylinder of radius (c) Cylinder of radius (d) All …

125. An inclined plane makes an angle of 30

An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to (a) g/3 (b) 2g/3 (c) …

118. A body rotating at 20 rad/sec is acted upon by a constant torque providing it a deceleration of 2 rad/sec

A body rotating at 20 rad/sec is acted upon by a constant torque providing it a deceleration of 2 rad/sec2. At what time will the body have kinetic energy same as the initial value if the torque continues to act …

112. A flywheel has moment of inertia 4 kg

A flywheel has moment of inertia 4 kg-m2 and has kinetic energy of 200 J. Calculate the number of revolutions it makes before coming to rest if a constant opposing couple of 5N-m is applied to the flywheel (a) 12.8 …

111. A wheel of moment of inertia 10 kg

A wheel of moment of inertia 10 kg-m2 is rotating at 10 rotations per minute. The work done in increasing its speed to 5 times its initial value, will be (a) 100 J (b) 131.4 J (c) 13.4 J (d) …

23.

The moment of inertia of a rod of length l about an axis passing through its centre of mass and perpendicular to rod is I. The moment of inertia of hexagonal shape formed by six such rods, about an axis …

22. Two identical rods each of mass M. and length l are joined in crossed position as shown in figure. The moment of inertia of this system about a bisector would be

(a) Ml2/6 (b) Ml2/12 (c) Ml2/3 (d) Ml2/4 Ans. b (29)

21. Three point masses each of mass are placed at the corners of an equilateral triangle of side a. Then the moment of inertia of this system about an axis passing along one side of the triangle is

(a) ma2 (b) 3 ma2 (c) 3/4 ma2 (d) 2/3 ma2 Ans. c (12)

26. Four spheres, each of mass and radius are situated at the four corners of square of side . The moment of inertia of the system about an axis perpendicular to the plane of square and passing through its centre will be

(a) (5/2)M (4r2 +5R2) (b) (2/5)M (4r2+5R2) (c) (2/5)M (4r2 +5r2) (d) (5/2)M (4r2 +5r2) Ans. b (20)

25. Four masses are joined to a light circular frame as shown in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be

(a) a/√2 (b) a/2 (c) a (d) 2a Ans. c (14)

Three rods each of length L and mass M are placed along X, Y and Z-axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is

(a) 2ML2/3 (b) 4 ML2/3 (c) 5 ML2/3 (d) ML2/3 Ans. a (12)

19. Let be the moment of inertia of an uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle θ with AB . The moment of inertia of the plate about the axis CD is then equal to

(a) l (b) l sin2θ (c) l cos2θ …

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

(a) 5 I (b) 6 I (c) 3 I (d) 4 I Ans. b (6)

14. Five particles of mass = 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

(a) 1 kg m2 (b) 0.1 kg m2 (c) 2 kg m2 (d) 0.2 kg m2 Ans. b (11)

155. A solid cube of side l is made to oscillate about a horizontal axis passing through one of its edges. Its time period will be

Ans. a (28)

154. A disc of radius R is made to oscillate about a horizontal axis passing through its periphery. Its time period would be

(a) 2π√(3R/2g) (b) 2π√(2R/3g (c) 2π√(R/g) (d) 2π√(2R/g) Ans. a (68)

153. A metre scale is suspended vertically from a horizontal axis passing through one end of it. Its time period would be

(a) 1.64 sec (b) 2 sec (c) 2.5 sec (d) 3.2 sec Ans. a (62)

152. In the above problem the angular velocity of the cylinder, after the masses fall down through distance h, will be

(a) 1/R√{(8 mgh)/(M+4m)} (b) 1/R√{8 mgh/(M+m)} (c) 1/R√{mgh/(M+m)} (d) 1/R √{8 mgh/(M+2m)} Ans. a (27)

147. A mass M is supported by a mass less string would wound a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with acceleration

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

151. A uniform solid cylinder of mass M and radius R rotates about a frictionless horizontal axle. Two similar masses suspended with the help two ropes wrapped around the cylinder. If the system is released from rest then the acceleration of each mass will be

(a) 4mg/M+2m (b) 4mg/M+4m (c) 2mg/M+m (d) 2mg/M+2m Ans. b (19)

150. A cylinder of mass M and radius r is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the cylinder and a bucket of mass m is suspended from the rope. The linear acceleration of the bucket will be

(a) Mg/M+2m (b) 2Mg/m+2M (c) Mg/2M+m (d) 2mg/M+2m Ans. d (88)

149. A massless string is wrapped round a disc of mass M and radius R. Another end is tied to a mass m which is initially at height h from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be

(a) √(2gh) (b) √(2gh)M/m (c) √(2ghm/M) (d) √(4mgh/2m+M) Ans. d (74)

148. A uniform disc of radius R and mass M can rotate on a smooth axis passing through its centre and perpendicular to its plane. A force F is applied on its rim. See fig. What is the tangential acceleration

(a) 2F/M (b) F/M (c) F/2M (d) F/4M Ans. a (37)

145. A disc of mass M and radius R rolls in a horizontal surface and then rolls up an inclined plane as shown in the fig. If the velocity of the disc is v, the height to which the disc will rise will be

(a) 3v2/ 2g (b) 3v2/4g (c) v2/4g (d) v2/2g Ans. b (56)

146.Two uniform similar discs roll down two inclined planes of length S and 2S respectively as shown is the fig. The velocities of two discs at the points A and B of the inclined planes are related as

(a) v1 = v2 (b) v1 =2v2 (c) v1 = v1 (v2/4) (d) v1 =( 3/4) v2 Ans. a (62)

144. A ring of radius 4a is rigidly fixed in vertical position on a table. A small disc of mass m and radius a is released as shown in the fig. When the disc rolls down, without slipping, to the lowest point of the ring, then its speed will be

(a) √ga (b) √2ga (c) √3ga (d) √4ga Ans. d (134)

142. A solid ball of mass m and radius r rolls without slipping along the track shown in the fig. The radius of the circular part of the track is R. The ball starts rolling down the track from rest from a height of 8R from the ground level. When the ball reaches the point P then its velocity will be

(a) √(gR) (b) √(5gR) (c) √(10gR) (d) √(3gR) Ans. c (21)

138. The acceleration of a body rolling down on an inclined plane does not depend upon

(a) Angle of inclination of the plane (b) Length of plane (c) Acceleration due to gravity of earth (d) Radius of gyration of body Ans. b (5)

136. A disc of radius R is rolling down an inclined plane whose angle of inclination is θ , Its acceleration would be

(a) 5/7 g sinθ (b) 2/3 g sinθ (c) 1/2 g sinθ (d) 3/5 g sinθ Ans. b (16)

135. A cylinder of mass M and radius R rolls on an inclined plane. The gain in kinetic energy is

(a) (1/2)Mv2 (b) (1/2) (c) (3/4)Mv2 (d) (3/4)Iω2 Ans. c (15)

134. A solid cylinder 30 cm in diameter at the top of an inclined plane 2.0 m high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is

(a) 5.29 m/sec (b) 4.1 × 103 m/sec (c) 51 m/sec (d) 51 cm/sec Ans. a (63)

The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll down an incline without slipping. If its angular velocity at the bottom be ω , then K.E. of the cylinder will be

(a) Iω2 (b) (3/2) Iω2 (c) 2Iω2 (d) (1/2)Iω2 Ans. b (48)

140. A ring is rolling on an inclined plane. The ratio of the linear and rotational kinetic energies will be

(a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 4 : 1 Ans. c (12)

139. A ring, a solid sphere, a disc and a solid cylinder of same radii roll down an inclined plane, which would reach the bottom in the last

(a) Ring (b) Disc (c) Solid sphere (d) Solid cylinder Ans. a (44)

137. A solid cylinder (i) rolls down (ii) slides down an inclined plane. The ratio of the accelerations in these conditions is

(a) 3 : 2 (b) 2 : 3 (c) √3:√2 (d) √2:√3 Ans. b (13)

133. From an inclined plane a sphere, a disc, a ring and a shell are rolled without slipping. The order of their reaching at the base will be

(a) Ring, shell, disc, sphere (b) Shell, sphere, disc, ring (c) Sphere, disc, shell, ring (d) Ring, sphere, disc, shell Ans.c (16)

131. A solid sphere, a solid cylinder, a disc and a ring are rolling down an inclined plane. Which of these bodies will reach the bottom simultaneously

(a) Solid sphere and solid cylinder (b) Solid cylinder and disc (c) Disc and ring (d) Solid sphere and ring Ans. b (29)

129. A body starts rolling down an inclined plane of length L and height h. This body reaches the bottom of the plane in time t. The relation between L and t is

(a) t∝L (b) t∝1/L (c) t∝L2 (d) t∝1/L2 Ans. a (34)

128. A solid cylinder of radius R and mass M, rolls down on inclined plane without slipping and reaches the bottom with a speed v. The speed would be less than v if we use

(a) A cylinder of same mass but of smaller radius (b) A cylinder of same mass but of larger radius (c) A cylinder of same radius but of smaller mass (d) A hollow cylinder of same mass and same radius …