Rotational Mechanics PYQs Set 5 (PDF)

Set 5 of 12 · Questions 121-150 of 343

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 5 (Q121-150)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
121. $The instantaneous angular position of a point on a rotating wheel is given by the equation Θ (t) = 2 t^{3} - 6 t^{2} The torque on the wheel becomes zero at$ (1) $t = 1 s$ (2) $t = 0.5 s$ (3) $t = 0.25 s$ (4) $t = 2 s$ 122. $A fan is rotating with an angular speed 300 rpm . The fan is switched off, and it takes 80 s to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is$ (1) $400$ (2) $200$ (3) $300$ (4) $314$ 123. $Moment of inertia (M . I .) of four bodies, having same mass and radius, are reported as - I_{1} = M . I . of thin circular ring about its diameter, I_{2} = M . I . of circular disc about an axis perpendicular to disc and going through the centre, I_{3} = M . I . of solid cylinder about its axis and I_{1} = M . I . of solid sphere about its diameter. Then :-$ (1) $I_{1} = I_{2} = I_{3} < I_{4}$ (2) $I_{1} + I_{2} = I_{3} + \frac{5}{2} I_{4}$ (3) $I_{1} + I_{3} < I_{2} + I_{4}$ (4) $I_{1} = I_{2} = I_{3} > I_{4}$ 124. $A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is$ (1) $\frac{1}{2}$ (2) $\frac{1}{6}$ (3) $\frac{7}{10}$ (4) $\frac{2}{7} .$ 125. $A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be$ (1) $0.5$ (2) $0.4$ (3) $0.8$ (4) $0.25$ 126. $Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :$ (1) $\frac{2 L}{5 m d ^{2}}$ (2) $\frac{4}{3} \frac{L}{m d ^{2}}$ (3) $\frac{3}{2} \frac{L}{m d ^{2}}$ (4) $\frac{2 L}{m d ^{2}}$ 127. $A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^{- 2} . Its net acceleration in m s^{- 2} at the end of 2.0 s is approximately$ (1) $6.0$ (2) $3.0$ (3) $8.0$ (4) $7.0$ 128. $The moment of inertia of a solid cylinder of mass M, length 2 R and radius R about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is I_{1} and about an axis passing through one end of the cylinder and perpendicular to the axis of the cylinder is I_{2}, then$ (1) $I_{2} < I_{1}$ (2) $I_{2} - I_{1} = M R^{2}$ (3) $\frac{I _{2}}{I _{1}} = \frac{19}{12}$ (4) $\frac{I _{2}}{I _{1}} = \frac{7}{6}$ 129. $A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as k θ^{2} . If its moment of inertia is I then the angular acceleration of the disc is$ (1) $\frac{k}{4 I} θ$ (2) $\frac{k}{I} θ$ (3) $\frac{k}{2 I} θ$ (4) $\frac{2 k}{I} θ$ 130. $Two coaxial discs, having moments of inertia I_{1} and \frac{I _{1}}{2}, are rotating with respective angular velocities ω_{1} and \frac{ω _{1}}{2} about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E_{f} and E_{i} are the final and initial total energies, then (E_{f} - E_{i}) is :$ (1) $- \frac{I _{1} ω _{1}^{2}}{12}$ (2) $\frac{I _{1} ω _{1}^{2}}{6}$ (3) $\frac{3}{8} I_{1} ω_{1}^{2}$ (4) $- \frac{I _{1} ω _{1}^{2}}{24}$ 131. $A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is . If radius of the ball be , then the fraction of total energy associated with its rotational energy will be$ (1) $\frac{K ^{2} + R ^{2}}{R ^{2}}$ (2) $\frac{K ^{2}}{R ^{2}}$ (3) $\frac{K ^{2}}{K ^{2} + R ^{2}}$ (4) $\frac{R ^{2}}{K ^{2} + R ^{2}}$ 132. $A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of$ (1) $10$ (2) $12$ (3) $4$ (4) $6.$ 133. $A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its center. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^{- 2} . Its net acceleration in ms^{- 2} at the end of 2.0 s is approximately [NEET 2016]$ (1) $8.0$ (2) $7.0$ (3) $6.0$ (4) $3.0$ 134. $A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v . The kinetic energy of the sphere at the bottom is$ (1) $\frac{1}{2} m v^{2}$ (2) $\frac{5}{3} m v^{2}$ (3) $\frac{2}{5} m v^{2}$ (4) $\frac{7}{10} m v^{2}$ 135. $A wheel having moment of inertia 40 kgm^{2} about its axis, rotates at 50 rpm . The angular retardation required to stop this wheel in 90 s is \dots\dots. rads^{- 2} .$ (1) $\frac{π}{45}$ (2) $\frac{π}{30}$ (3) $\frac{π}{54}$ (4) $\frac{π}{24}$ 136. $The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are$ (1) $1: 2$ (2) $3: 2$ (3) $2: 1$ (4) $2 : 1$ 137. $Moon revolves around the earth in an orbit of radius R with time period of revolution T. It also rotates about its own axis with a time period T . If mass of the moon is M and its radius is 'r', the total kinetic energy of the moon is$ (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) $\frac{M π ^{2} R ^{2}}{2 T ^{2}} + \frac{4 M r ^{2} π ^{2}}{5 T ^{2}}$ 138. $A solid sphere rolls down without slipping on a smooth inclined plane of inclination sin^{- 1} (0.42) . If the acceleration due to gravity is 10 ms^{- 2}, the acceleration of the rolling sphere is$ (1) $1 ms^{- 2}$ (2) $2 ms^{- 2}$ (3) $3 ms^{- 2}$ (4) $4 ms^{- 2}$ 139. $The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is$ (1) $2 : 1$ (2) $2 : 3$ (3) $3 : 2$ (4) $1: 2$ 140. $A solid sphere of mass 2 kg is rolling on a friction horizontal surface with velocity 6 m / s . It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring - 36 N / m).$ (1) $14 m$ (2) $2.8 m$ (3) $1.4 m$ (4) $0.7 m$ 141. $Two cars A and B each of mass 10^{3} kg are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds 72 km / h and 36 km / h . The magnitude of angular momentum of carA with respect to carB is____J.s.$ (1) $2 \times 10^{5}$ (2) $10^{5}$ (3) $3.6 \times 10^{5}$ (4) $3 \times 10^{5}$ 142. $The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm^{2} . The length of the 400 g rod is nearly [NEET 2024]$ (1) $8.5 cm$ (2) $17.5 cm$ (3) $20.7 cm$ (4) $72.0 cm$ 143. $Find the torque about the origin when a force of 3 j N acts on the particle whose position vector is 2 k m . [NEET 2020]$ (1) $6 j N - m$ (2) $- 6 i N - m$ (3) $6 k N - m$ (4) $6 i N - m$ 144. $A hollow sphere of mass ' M' and radius ' R' is rotating with angular frequency ' ω'. It suddenly stops rotating and 75 % of kinetic energy is converted to heat. If ' S' is the specific heat of the material in J / kgK then rise in temperature of the sphere is (M.I. of hollow sphere = \frac{2}{3} M R^{2})$ (1) $\frac{Rω}{4 S}$ (2) $\frac{R ^{2} ω ^{2}}{4 S}$ (3) $\frac{Rω}{2 S}$ (4) $\frac{R ^{2} ω ^{2}}{2 S}$ 145. $A fly wheel starts from rest and rotates at a constant acceleration of 2 rad s^{- 2} . The number of revolutions that it makes in first 10 s is$ (1) $16$ (2) $24$ (3) $32$ (4) $8$ 146. $A thin disc of mass M and radius R has mass per unit area σ (r) = k r^{2} where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :$ (1) $\frac{MR ^{2}}{3}$ (2) $\frac{2 MR ^{2}}{3}$ (3) $\frac{MR ^{2}}{6}$ (4) $\frac{MR ^{2}}{2}$ 147. $A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω . If another disc of same dimensions but of mass M /2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :$ (1) $\frac{3}{2} ω$ (2) $\frac{5}{4} ω$ (3) $\frac{2}{3} ω$ (4) $\frac{4}{5} ω$ 148. $Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio$ (1) $2 : 1$ (2) $1 : 2$ (3) $2 : 1$ (4) $1: 2$ 149. $The torque due to the force (2 i + j + 2 k) about the origin, acting on a particle whose position vector is (i + j + k), would be$ (1) $i - k$ (2) $i + k$ (3) $j + k$ (4) $i - j + k$ 150. $A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s . What is the angular acceleration assuming to be uniform?$ (1) $2 π rad s^{- 2}$ (2) $60 π rad s^{- 2}$ (3) $40 π rad s^{- 2}$ (4) $90 π rad s^{- 2}$