Rotational Mechanics PYQs Set 5 (PDF)

Set 5 of 14 · Questions 121-150 of 410

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

Mere Teacher · Previous Year Questions JEE Main 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. $Which of the following are correct expression for torque acting on a body? (A0 τ=r\timesL(B) τ = \frac{d}{dt} (r \times p) (C) τ = r \times \frac{d p}{dt} (D) τ=Iα(E.)τ=r\timesF(r = position vector; p = linear momentum; L = angular momentum; α = angularacceleration; I = moment of inertia; F = force; t = time) Choose the correct answer from the options given below:$ (1) $A, B, D and E Only$ (2) $C and D Only$ (3) $B, C, D and E Only$ (4) $B, D and E Only$ 122. $A body of mass 5 kg acquires an acceleration of 10 rad s^{- 2} due to an applied torque of 2 Nm . Its radius of gyrations is$ (1) $2.5 m$ (2) $2.5 m$ (3) $0.2 m$ (4) $0.2 m$ 123. $Let M be the mass and L be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is$ (1) $1$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $\frac{1}{8}$ 124. $A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder ' a_{c}' to that of sphere ' a_{s}' is$ (1) $\frac{11}{15}$ (2) $\frac{13}{14}$ (3) $\frac{15}{14}$ (4) $\frac{14}{15}$ 125. $When the position vector r = x i + y j + z k changes sign as - r, which one of the following vector will not flip under sign change ?$ (1) $Angular momentum$ (2) $Velocity$ (3) $Acceleration$ (4) $Linear momentum$ 126. $A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_{t}) as well as rotational kinetic energy (K_{r}) simultaneously. The ratio K_{t} : (K_{t} + K_{r}) for the sphere is [NEET 2018]$ (1) $10 : 7$ (2) $5 : 7$ (3) $7 : 10$ (4) $2 : 5$ 127. $A uniform disc of mass 100 kg and radius 2 m is rotating at 1 rad / s about a perpendicular axis passing through its centre. A boy of mass 60 kg standing at the centre of the disk suddenly jumps to a point which is 1 m from the centre of the disc. The final angular velocity of the boy (in rad/s) is$ (1) $0.77$ (2) $0.5$ (3) $41$ (4) $2$ 128. $Moment of inertia of a body about a given axis is 1.5 kg m^{2} . Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad / s^{2} must be applied about the axis for a duration of:$ (1) $2.5 s$ (2) $2 s$ (3) $5 s$ (4) $3 s$ 129. $The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is$ (1) $6 π rad / s^{2}$ (2) $2 π rad / s^{2}$ (3) $8 π rad / s^{2}$ (4) $4 π rad / s^{2}$ 130. $A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its center of mass has speed of 20 cm / s . How much work is needed to stop it? [NEET 2019]$ (1) $30 KJ$ (2) $2 J$ (3) $1 J$ (4) $3 J$ 131. $A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 π revolutions is [NEET 2019]$ (1) $2 \times 10^{- 3} N - m$ (2) $12 \times 10^{- 4} N - m$ (3) $2 \times 10^{6} N - m$ (4) $2 \times 10^{- 6} N - m$ 132. $A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia% out the axle is 200 kg m^{2} . It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s^{- 1} relative to the ground. Time taken by the man to complete one revolution is$ (1) $πs$ (2) $\frac{3 π}{2} s$ (3) $2 πs$ (4) $\frac{π}{2} s$ 133. $The instantaneous angular position of a point on a rotating wheel is given by the equation Θ (t) = 2 t^{3} - 6 t^{2} The torque on the wheel becomes zero at$ (1) $t = 1 s$ (2) $t = 0.5 s$ (3) $t = 0.25 s$ (4) $t = 2 s$ 134. $A fan is rotating with an angular speed 300 rpm . The fan is switched off, and it takes 80 s to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is$ (1) $400$ (2) $200$ (3) $300$ (4) $314$ 135. $Moment of inertia (M . I .) of four bodies, having same mass and radius, are reported as - I_{1} = M . I . of thin circular ring about its diameter, I_{2} = M . I . of circular disc about an axis perpendicular to disc and going through the centre, I_{3} = M . I . of solid cylinder about its axis and I_{1} = M . I . of solid sphere about its diameter. Then :-$ (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) $I_{1} = I_{2} = I_{3} > I_{4}$ 136. $A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is$ (1) $\frac{1}{2}$ (2) $\frac{1}{6}$ (3) $\frac{7}{10}$ (4) $\frac{2}{7} .$ 137. $A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be$ (1) $0.5$ (2) $0.4$ (3) $0.8$ (4) $0.25$ 138. $Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :$ (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) $\frac{2 L}{m d ^{2}}$ 139. $A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^{- 2} . Its net acceleration in m s^{- 2} at the end of 2.0 s is approximately$ (1) $6.0$ (2) $3.0$ (3) $8.0$ (4) $7.0$ 140. $The moment of inertia of a solid cylinder of mass M, length 2 R and radius R about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is I_{1} and about an axis passing through one end of the cylinder and perpendicular to the axis of the cylinder is I_{2}, then$ (1) $I_{2} < I_{1}$ (2) $I_{2} - I_{1} = M R^{2}$ (3) $\frac{I _{2}}{I _{1}} = \frac{19}{12}$ (4) $\frac{I _{2}}{I _{1}} = \frac{7}{6}$ 141. $A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as k θ^{2} . If its moment of inertia is I then the angular acceleration of the disc is$ (1) $\frac{k}{4 I} θ$ (2) $\frac{k}{I} θ$ (3) $\frac{k}{2 I} θ$ (4) $\frac{2 k}{I} θ$ 142. $Two coaxial discs, having moments of inertia I_{1} and \frac{I _{1}}{2}, are rotating with respective angular velocities ω_{1} and \frac{ω _{1}}{2} about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E_{f} and E_{i} are the final and initial total energies, then (E_{f} - E_{i}) is :$ (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) $- \frac{I _{1} ω _{1}^{2}}{24}$ 143. $A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is . If radius of the ball be , then the fraction of total energy associated with its rotational energy will be$ (1) $\frac{K ^{2} + R ^{2}}{R ^{2}}$ (2) $\frac{K ^{2}}{R ^{2}}$ (3) $\frac{K ^{2}}{K ^{2} + R ^{2}}$ (4) $\frac{R ^{2}}{K ^{2} + R ^{2}}$ 144. $A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of$ (1) $10$ (2) $12$ (3) $4$ (4) $6.$ 145. $A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its center. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s^{- 2} . Its net acceleration in ms^{- 2} at the end of 2.0 s is approximately [NEET 2016]$ (1) $8.0$ (2) $7.0$ (3) $6.0$ (4) $3.0$ 146. $A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v . The kinetic energy of the sphere at the bottom is$ (1) $\frac{1}{2} m v^{2}$ (2) $\frac{5}{3} m v^{2}$ (3) $\frac{2}{5} m v^{2}$ (4) $\frac{7}{10} m v^{2}$ 147. $A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be_____rad s^{- 2} .$ 148. $A solid sphere with uniform density and radius R is rotating initially with constant angular velocity (ω_{1}) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become R /2 is x ω_{1} . The value of x is______.$ 149. $The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of F = i - j + k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is .$ 150. $A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \frac{7}{x} where x is______$