Rotational Mechanics PYQs Set 6 (PDF)

Set 6 of 12 · Questions 151-180 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 6 (Q151-180)
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.
151. $A tube of length L is filled completely with an incompressible liquid ofmass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω The force exerted by the liquid at the other end is$ (1) $\frac{M L ^{2} ω ^{2}}{2}$ (2) $ML ω^{2} 2$ (3) $\frac{M L ^{2} ω}{2}$ (4) $ML ω^{2}$ 152. $The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is ' I'. It is rotating with angular velocity ' ω'. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis, then loss in kinetic energy is$ (1) $\frac{I ω ^{2}}{2}$ (2) $\frac{I ω ^{2}}{4}$ (3) $\frac{I ω ^{2}}{6}$ (4) $\frac{I ω ^{2}}{8}$ 153. $Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm . When released from rest the heavier mass is observed to fall 81 cm in 9 s . The rotational inertia of the pulley is____kg \cdot m^{2} . (g = 9.8 m / s^{2})$ (1) $4.75 \times 10^{- 3}$ (2) $9.5 \times 10^{- 3}$ (3) $1.86 \times 10^{- 2}$ (4) $8.3 \times 10^{- 3}$ 154. $Find the torque of a force F = - 3 i + j + 5 k acting at the point r = 7 i + 3 j + k .$ (1) $- 21 i + 4 j + 4 k$ (2) $- 14 i + 34 j - 16 k$ (3) $14 i - 38 j + 16 k$ (4) $4 i + 4 j + 6 k .$ 155. $A solid sphere of mass 2 kg is rolling without slipping on a horizontal surface with a velocity 5 ms^{- 1} . The rotational kinetic energy of the sphere is$ (1) $25 J$ (2) $12.5 J$ (3) $10 J$ (4) $20 J$ 156. $The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t3 - 6t2 . The torque on the wheel becomes zero at :$ (1) $t = 1s$ (2) $t = 0.5 s$ (3) $t = 0.25 s$ (4) $t = 2s$ 157. $The moment of inertia of a circular ring of radius r and mass M about diameter is$ (1) $\frac{2}{5} M r^{2}$ (2) $\frac{M r ^{2}}{4}$ (3) $\frac{M r ^{2}}{2}$ (4) $\frac{M r ^{2}}{12}$ 158. $The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_{0} . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is$ (1) $I_{0} + M L^{2} /2$ (2) $I_{0} + M L^{2} /4$ (3) $I_{0} + 2 M L^{2}$ (4) $I_{0} + M L^{2}$ 159. $Moment of inertia of a uniform circular disc about a diameter is I . Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be$ (1) $5 I$ (2) $3 I$ (3) $6 I$ (4) $4 I$ 160. $A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes (1/4)^{th} of the original in time t and n revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)$ (1) $\frac{4 n}{15}$ (2) $\frac{8 n}{15}$ (3) $\frac{16 n}{15}$ (4) $\frac{32 n}{15}$ 161. $The time dependence of the position of a particle of mass m = 2 is given by r \to (t) = 2 t i^- 3 t^{2} j^. Its angular momentum, with respect to the origin, at time t = 2 is :$ (1) $48 (i^+ j^)$ (2) $36 k^$ (3) $- 34 (k^- i^)$ (4) $- 48 k^$ 162. $For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier?$ (1) $solid cylinder$ (2) $hollow cylinder$ (3) $both simultaneously$ (4) $can’t say anything.$ 163. $Moment of inertia of a body about two perpendicular axes X and Y in the plane of lamina are 20 kg m^{2} and 25 kg m^{2} respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of X and Y axes is$ (1) $5 kg m^{2}$ (2) $45 kg m^{2}$ (3) $12.5 kg m^{2}$ (4) $500 kg m^{2}$ 164. $A thin metal wire of length Land uniform linear mass density ρ is bent into a circular coil with O as centre. The moment of inertia of a coil about the axis X X^{’} is$ (1) $3 ρ L^{3} /8 π^{2}$ (2) $ρ L^{3} /4 π^{2}$ (3) $3 ρ L^{2} /4 π^{2}$ (4) $ρ L^{3} /8 π^{2}$ 165. $A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is :$ (1) $\frac{1}{4} v i^+ \frac{3}{2} v j^$ (2) $\frac{1}{3} v i^+ \frac{2}{3} v j^$ (3) $\frac{2}{3} v i^+ \frac{1}{3} v j^$ (4) $\frac{3}{2} v i^+ \frac{1}{4} v j^$ 166. $A block of mass m = 1 kg slides with velocity v = 6m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M = 2kg and length I = lm, the value of θ is approximately (take g = 10m/s²)$ (1) $49°$ (2) $55°$ (3) $63°$ (4) $69°$ 167. $Two discs have moments of intertia I_{1} and I_{2} about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω_{1} and ω_{2} respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :$ (1) $\frac{I _{1} I _{2}}{( I _{1} + I _{2} )} (ω_{1} - ω_{2})^{2}$ (2) $\frac{( I _{1} - I _{2} ) ^{2} ω _{1} ω _{2}}{2 ( I _{1} + I _{2} )}$ (3) $\frac{I _{1} I _{2}}{2 ( I _{1} + I _{2} )} (ω_{1} - ω_{2})^{2}$ (4) $\frac{( ω _{1} - ω _{2} ) ^{2}}{2 ( I _{1} + I _{2} )}$ 168. $A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will$ (1) $decrease by a factor of 2$ (2) $remain constant$ (3) $increase by a factor of 2$ (4) $increase by a factor of 4$ 169. $A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s^{- 2} is$ (1) $25 N$ (2) $50 N$ (3) $78.5 N$ (4) $157 N$ 170. $Three identical spherical shells, cach of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three sphereical shell about XX' axis is :$ (1) $3 mr2$ (2) $\frac{16}{5} m r^{2}$ (3) $4 mr2$ (4) $\frac{11}{5} m r^{2}$ 171. $Four spheres each of diameter 2 a and mass m are placed in a way that their centres lie on the four corners of a square of side b . Moment of inertia of the system about an axis along one of the sides of the square is$ (1) $\frac{8}{5} m a^{2}$ (2) $\frac{4}{5} m a^{2} + 5 m b^{2}$ (3) $\frac{4}{5} m a^{2} + 2 m b^{2}$ (4) $\frac{8}{5} m a^{2} + 2 m b^{2}$ 172. $The moment of inertia of a circular disc of radius 2 m and mass 1 kg about an axis passing through the centre of mass but perpendicular to the plane of the disc is 2 kg m^{2} . Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (See the given figure).$ (1) $8 kg m^{2}$ (2) $4 kg m^{2}$ (3) $10 kg m^{2}$ (4) $6 kg m^{2}$ 173. $A circular platform is mounted on a frictionless vertical axle. Its radius R = 2m and its moment of inertia about the axle is 200 kgm2. it is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1ms-1 relative to the ground. Time taken by the man to complete one revolution is :$ (1) $π s$ (2) $\frac{3 π}{2} s$ (3) $2π s$ (4) $\frac{π}{2} s$ 174. $The torque of a force 5 i^+ 3 j^- 7 k^about the origin is τ . If the force acts on a particle whose position vector is 2 i^+ 2 j^+ k^, then the value of τ will be :$ (1) $11 i^+ 19 j^- 4 k^$ (2) $- 11 i^+ 9 j^- 16 k^$ (3) $- 17 i^+ 19 j^- 4 k^$ (4) $17 i^+ 9 j^+ 16 k^$ 175. $A solid sphere of mass m = 500 gm is rolling without slipping on a horizontal surface. Find kinetic energy of a sphere if velocity of centre of mass is 5 cm/ sec.$ (1) $\frac{35}{2} \times 1 0^{- 4} J$ (2) $\frac{35}{4} \times 1 0^{- 4} J$ (3) $35 \times 10^{- 4} J$ (4) $35 \times 10^{- 3} J$ 176. $A sphere of mass 2 kg and radius is rolling 0.5 m with an initial speed of 1 ms^{- 1} goes up an inclined plane which makes an angle of 30^{\circ} with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ?$ (1) $0.60 s$ (2) $0.52 s$ (3) $0.57 s$ (4) $0.80 s$ 177. $As shown in the figure, a bob a mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be :$ (1) $r \frac{3}{4 g h}$ (2) $\frac{1}{r} \frac{2 g h}{3}$ (3) $r \frac{3}{2 g h}$ (4) $\frac{1}{r} \frac{4 g h}{3}$ 178. $Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is$ (1) $\frac{2}{3} M l^{2}$ (2) $\frac{13}{3} M l^{2}$ (3) $\frac{1}{3} M l^{2}$ (4) $\frac{4}{3} M l^{2}$ 179. $Moment of inertia of a square plate of side about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:$ (1) $\frac{M l ^{2}}{6}$ (2) $M l^{2}$ (3) $\frac{M l ^{2}}{12}$ (4) $\frac{2}{3} M l^{2}$ 180. $Three point masses each of mass m are kept at the corners of an equilateral triangle of side L . The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to (cos 30^{\circ} = sin 60^{\circ} = 3 /2)$ (1) $L$ (2) $L^{3/2}$ (3) $L$ (4) $L^{- 2}$