Rotational Mechanics PYQs Set 6 (PDF)

Set 6 of 14 · Questions 151-180 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 6 (Q151-180)
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151. $A wheel having moment of inertia 40 kgm^{2} about its axis, rotates at 50 rpm . The angular retardation required to stop this wheel in 90 s is \dots\dots. rads^{- 2} .$ (1) $\frac{π}{45}$ (2) $\frac{π}{30}$ (3) $\frac{π}{54}$ (4) $\frac{π}{24}$ 152. $The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are$ (1) $1: 2$ (2) $3: 2$ (3) $2: 1$ (4) $2 : 1$ 153. $Moon revolves around the earth in an orbit of radius R with time period of revolution T. It also rotates about its own axis with a time period T . If mass of the moon is M and its radius is 'r', the total kinetic energy of the moon is$ (1) $\frac{2 M π ^{2} R ^{2}}{T ^{2}} + \frac{4 M r ^{2} π ^{2}}{5 T ^{2}}$ (2) $\frac{M π ^{2} R ^{2}}{2 T ^{2}}$ (3) $\frac{4 M r ^{2} π ^{2}}{5 T ^{2}}$ (4) $\frac{M π ^{2} R ^{2}}{2 T ^{2}} + \frac{4 M r ^{2} π ^{2}}{5 T ^{2}}$ 154. $A solid sphere rolls down without slipping on a smooth inclined plane of inclination sin^{- 1} (0.42) . If the acceleration due to gravity is 10 ms^{- 2}, the acceleration of the rolling sphere is$ (1) $1 ms^{- 2}$ (2) $2 ms^{- 2}$ (3) $3 ms^{- 2}$ (4) $4 ms^{- 2}$ 155. $The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is$ (1) $2 : 1$ (2) $2 : 3$ (3) $3 : 2$ (4) $1: 2$ 156. $A solid sphere of mass 2 kg is rolling on a friction horizontal surface with velocity 6 m / s . It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring - 36 N / m).$ (1) $14 m$ (2) $2.8 m$ (3) $1.4 m$ (4) $0.7 m$ 157. $Two cars A and B each of mass 10^{3} kg are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds 72 km / h and 36 km / h . The magnitude of angular momentum of carA with respect to carB is____J.s.$ (1) $2 \times 10^{5}$ (2) $10^{5}$ (3) $3.6 \times 10^{5}$ (4) $3 \times 10^{5}$ 158. $The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm^{2} . The length of the 400 g rod is nearly [NEET 2024]$ (1) $8.5 cm$ (2) $17.5 cm$ (3) $20.7 cm$ (4) $72.0 cm$ 159. $Find the torque about the origin when a force of 3 j N acts on the particle whose position vector is 2 k m . [NEET 2020]$ (1) $6 j N - m$ (2) $- 6 i N - m$ (3) $6 k N - m$ (4) $6 i N - m$ 160. $A hollow sphere of mass ' M' and radius ' R' is rotating with angular frequency ' ω'. It suddenly stops rotating and 75 % of kinetic energy is converted to heat. If ' S' is the specific heat of the material in J / kgK then rise in temperature of the sphere is (M.I. of hollow sphere = \frac{2}{3} M R^{2})$ (1) $\frac{Rω}{4 S}$ (2) $\frac{R ^{2} ω ^{2}}{4 S}$ (3) $\frac{Rω}{2 S}$ (4) $\frac{R ^{2} ω ^{2}}{2 S}$ 161. $A fly wheel starts from rest and rotates at a constant acceleration of 2 rad s^{- 2} . The number of revolutions that it makes in first 10 s is$ (1) $16$ (2) $24$ (3) $32$ (4) $8$ 162. $A thin disc of mass M and radius R has mass per unit area σ (r) = k r^{2} where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :$ (1) $\frac{MR ^{2}}{3}$ (2) $\frac{2 MR ^{2}}{3}$ (3) $\frac{MR ^{2}}{6}$ (4) $\frac{MR ^{2}}{2}$ 163. $A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω . If another disc of same dimensions but of mass M /2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :$ (1) $\frac{3}{2} ω$ (2) $\frac{5}{4} ω$ (3) $\frac{2}{3} ω$ (4) $\frac{4}{5} ω$ 164. $Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio$ (1) $2 : 1$ (2) $1 : 2$ (3) $2 : 1$ (4) $1: 2$ 165. $The torque due to the force (2 i + j + 2 k) about the origin, acting on a particle whose position vector is (i + j + k), would be$ (1) $i - k$ (2) $i + k$ (3) $j + k$ (4) $i - j + k$ 166. $A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s . What is the angular acceleration assuming to be uniform?$ (1) $2 π rad s^{- 2}$ (2) $60 π rad s^{- 2}$ (3) $40 π rad s^{- 2}$ (4) $90 π rad s^{- 2}$ 167. $A tube of length L is filled completely with an incompressible liquid ofmass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω The force exerted by the liquid at the other end is$ (1) $\frac{M L ^{2} ω ^{2}}{2}$ (2) $ML ω^{2} 2$ (3) $\frac{M L ^{2} ω}{2}$ (4) $ML ω^{2}$ 168. $The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is ' I'. It is rotating with angular velocity ' ω'. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis, then loss in kinetic energy is$ (1) $\frac{I ω ^{2}}{2}$ (2) $\frac{I ω ^{2}}{4}$ (3) $\frac{I ω ^{2}}{6}$ (4) $\frac{I ω ^{2}}{8}$ 169. $Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm . When released from rest the heavier mass is observed to fall 81 cm in 9 s . The rotational inertia of the pulley is____kg \cdot m^{2} . (g = 9.8 m / s^{2})$ (1) $4.75 \times 10^{- 3}$ (2) $9.5 \times 10^{- 3}$ (3) $1.86 \times 10^{- 2}$ (4) $8.3 \times 10^{- 3}$ 170. $Find the torque of a force F = - 3 i + j + 5 k acting at the point r = 7 i + 3 j + k .$ (1) $- 21 i + 4 j + 4 k$ (2) $- 14 i + 34 j - 16 k$ (3) $14 i - 38 j + 16 k$ (4) $4 i + 4 j + 6 k .$ 171. $A solid sphere of mass 2 kg is rolling without slipping on a horizontal surface with a velocity 5 ms^{- 1} . The rotational kinetic energy of the sphere is$ (1) $25 J$ (2) $12.5 J$ (3) $10 J$ (4) $20 J$ 172. $The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t3 - 6t2 . The torque on the wheel becomes zero at :$ (1) $t = 1s$ (2) $t = 0.5 s$ (3) $t = 0.25 s$ (4) $t = 2s$ 173. $The moment of inertia of a circular ring of radius r and mass M about diameter is$ (1) $\frac{2}{5} M r^{2}$ (2) $\frac{M r ^{2}}{4}$ (3) $\frac{M r ^{2}}{2}$ (4) $\frac{M r ^{2}}{12}$ 174. $The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_{0} . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is$ (1) $I_{0} + M L^{2} /2$ (2) $I_{0} + M L^{2} /4$ (3) $I_{0} + 2 M L^{2}$ (4) $I_{0} + M L^{2}$ 175. $Moment of inertia of a uniform circular disc about a diameter is I . Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be$ (1) $5 I$ (2) $3 I$ (3) $6 I$ (4) $4 I$ 176. $A force F = 4 i + 3 j + 4 k is applied on an intersection point of x = 2 plane and x - axis. The magnitude oftorque of this force about a point (2, 3, 4) is(Round off to the Nearest Integer)$ 177. $Two masses m and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius r = 0.1 m . The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2 m mass is released from rest and its speed when it has descended through a height of 3.6 m is____m/s. (Assume string does not slip and g = 10 m / s^{2})$ 178. $A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s^{- 1} . If the moment of inertia of the sphere about its tangent is x x 1 0^{- 2} times its angular momentum about the diameter. Then the value of x will be$ 179. $The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number ofrevolutions by the truck engine during this time is___ (Assuming the acceleration to be uniform).$ 180. $A force F = (i + 2 j + 3 k) N acts at a point (4 i + 3 j - 3 k) m . Then the magnitude of torque aboutthe point (i + 2 j + k) m will be x N - m . The value of x is :$