Rotational Mechanics PYQs Set 1 (PDF)

Set 1 of 12 · Questions 1-30 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 1 (Q1-30)
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1. $Two discs of same mass and same thickness (t) are made from two different matcrials of densities ' d_{1}' and ' d_{2}' respectively. The ratio of the moment of inertia I_{1} to I_{2} of two discs about an axis passing through the centre and perpendicular to the plane of disc is$ (1) $d_{1} : d_{2}$ (2) $d_{2} : d_{1}$ (3) $1 : d_{1} d_{2}$ (4) $1 : d_{1}^{2} d_{2}$ 2. $The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is$ (1) $2 : 3$ (2) $2 : 1$ (3) $5 : 6$ (4) $1: 2$ 3. $A particle starting from rest, moves in a circle of radius^{’} r'. It attains a velocity of v_{0} m / s in the n th round. Its angular acceleration will be [NEET 2019]$ (1) $\frac{v _{0}}{n} rad / s^{2}$ (2) $\frac{v _{0}^{2}}{2 πn r ^{2}} rad / s^{2}$ (3) $\frac{v _{0}^{2}}{4 πn r ^{2}} rad / s^{2}$ (4) $\frac{v _{0}^{2}}{4 πnr} rad / s^{2}$ 4. $A solid homogenous sphere of mass M and radius is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere$ (1) $total kinetic energy is conserved$ (2) $the angular momentum of the sphere about the point of contact with the plane is conserved$ (3) $only the rotational kinetic energy about the centre of mass is conserved$ (4) $angular momentum about the centre of mass is conserved$ 5. $The ratio of angular speed of hour hand of a watch to the angular speed of earth's rotation about its axis, is$ (1) $2 : 1$ (2) $4 : 1$ (3) $5 : 1$ (4) $3 : 1$ 6. $A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30^{\circ}, then the angle of inclination of plane B must be (approximately)$ (1) $60^{\circ}$ (2) $53^{\circ}$ (3) $45^{\circ}$ (4) $37^{\circ}$ 7. $Three objects, A : (a solid sphere), B : (a thin circular disc) and C : (a circular ring), each have the same mass M and radius R . They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation [NEET 2018]$ (1) $W_{B} > W_{A} > W_{C}$ (2) $W_{A} > W_{B} > W_{C}$ (3) $W_{C} > W_{B} > W_{A}$ (4) $W_{A} > W_{C} > W_{B}$ 8. $If F is the force acting on a particle having position vector y and τ be the torque of this force about the origin, then$ (1) $r \cdot τ > 0 and F \cdot τ < 0$ (2) $r \cdot τ = 0 and F \cdot τ = 0$ (3) $r \cdot r = 0 and F \cdot r \neq = 0$ (4) $r \cdot τ \neq = 0 and F \cdot τ = 0$ 9. $Two rotating bodies A and B of masses m and 2 m with moments of inertia I_{A} and I_{B} (I_{B} > I_{A}) have equal kinetic energy of rotation. If L_{A} and L_{B} be their angular momenta respectively, then$ (1) $L_{A} = \frac{L _{B}}{2}$ (2) $L_{A} = 2 L_{B}$ (3) $L_{B} > L_{A}$ (4) $L_{A} > L_{B}$ 10. $A disc is rotating with angular speed 00. If a child sits on it, what is conserved?$ (1) $linear momentum$ (2) $angular momentum$ (3) $kinetic energy$ (4) $potential energy.$ 11. $Consider two uniform discs of the same thickness and different radii R_{1} = R and R_{2} = αR made of the same material. If the ratio of their moments of inertia I_{1} and I_{2}, respectively, about their axes is I_{1} : I_{2} = 1 : 16 then the value of α is:$ (1) $2$ (2) $4$ (3) $22$ (4) $2$ 12. $If an energy of 684 J is needed to increase the speed of a flywheel from 180 rpm to 360 rpm, then find its moment of inertia.$ (1) $0.7 kg / m^{2}$ (2) $1.28 kg / m^{2}$ (3) $2.75 kg / m^{2}$ (4) $7.28 kg / m^{2}$ 13. $When a 12000 joule of work is done on a flywheel, its frequency of rotation increases from 10 to 20 Hz . The moment of inertia of flywheel about its axis of rotation is (π^{2} = 10)$ (1) $1 kg m^{2}$ (2) $2 kg m^{2}$ (3) $1.688 kg m^{2}$ (4) $1.5 kg m^{2}$ 14. $An object undergoing simple harmonic motion takes 0.5 s to travel from one point of zero velocity to the next such point. The angular frequency of the motion is$ (1) $π rad s^{- 1}$ (2) $2 π rad s^{- 1}$ (3) $3 π rad s^{- 1}$ (4) $\frac{π}{2} rad s^{- 1}$ 15. $The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius R, (ii) a solid cylinder of radius \frac{R}{2} and (iii) a solid sphere of radius \frac{R}{4} . If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is :$ (1) $4 : 3 : 2$ (2) $20 : 15 : 14$ (3) $14 : 15 : 20$ (4) $2 : 3 : 4$ 16. $In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is$ (1) $5$ (2) $2$ (3) $0.5$ (4) $0.2$ 17. $A thin smooth rod of length L and mass M is rotating freely with angular speed ω_{0} about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be:$ (1) $\frac{M ω _{0}}{M + m}$ (2) $\frac{M ω _{0}}{M + 3 m}$ (3) $\frac{M ω _{0}}{M + 6 m}$ (4) $\frac{M ω _{0}}{M + 2 m}$ 18. $A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?$ (1) $0.25 rad s^{- 2}$ (2) $25 rad s^{- 2}$ (3) $5 m s^{- 2}$ (4) $25 m s^{- 2}$ 19. $A solid sphere of 100 kg and radius 10 m moving in a space becomes a circular disc of radius 20 m in one hour. Then the rate of change of moment of inertia in the process is$ (1) $\frac{40}{9} kg m^{2} s^{- 1}$ (2) $\frac{10}{9} kg m^{2} s^{- 1}$ (3) $\frac{50}{9} kg m^{2} s^{- 1}$ (4) $\frac{25}{9} kg m^{2} s^{- 1}$ 20. $The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in 14 s. Its angular acceleration is [NEET 2020]$ (1) $2 π rad / s^{2}$ (2) $28 π rad / s^{2}$ (3) $120 π rad / s^{2}$ (4) $1 rad / s^{2}$ 21. $For a particle moving in vertical circle, the total energy at different positions along the path$ (1) $is conserved$ (2) $increases$ (3) $decreases$ (4) $may increase or decrease$ 22. $A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (E_{sphere} / E_{cylinder}) will be [NEET 2016]$ (1) $2 : 3$ (2) $1 : 5$ (3) $1 : 4$ (4) $3 : 1$ 23. $From a circular ring of mass M and radius R, an arc corresponding to a 90^{\circ} sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is K times M R^{2} . Then, the value of K is [NEET 2021]$ (1) $\frac{3}{4}$ (2) $\frac{7}{8}$ (3) $\frac{1}{4}$ (4) $\frac{1}{8}$ 24. $A force F = 5 i + 2 j - 5 k acts on a particle whose position vector is r = i - 2 j + k . What is the torque about the origin?$ (1) $8 i - 10 j - 8 k$ (2) $8 i + 10 j + 12 k$ (3) $10 i - 10 j - k$ (4) $8 i + 10 j - 12 k$ 25. $A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by 9 % . The change in its angular speed is$ (1) $increases by 9 %$ (2) $decreases by 9 %$ (3) $increases by 6 %$ (4) $decreases by 6 %$ 26. $A fly wheel at rest is to reach an angular velocity of 24 rad / s in 8 second with constant angular acceleration. The total angle turned through during this interval is$ (1) $24 rad$ (2) $48 rad$ (3) $72 rad q$ (4) $96 rad$ 27. $A square lamina of side ' b' has same mass as a disc of radius ' R', the moment of inertia of the two objecte about an axis perpendicular to the plane and passing through the centre is equal. The ratio b/R is$ (1) $1 : 1$ (2) $3 : 1$ (3) $6 : 1$ (4) $1 : 3$ 28. $Two rotating bodies A and B of masses m and 2m with moments of inertia I_{A} and I_{B} (I_{B} > I_{A}) have equal kinetic energy of rotation. If L_{A} and L_{B} be their angular momenta respectively, then$ (1) $L_{A} > L_{B}$ (2) $L_{A} = \frac{L _{B}}{2}$ (3) $L_{A} = 2 L_{B}$ (4) $L_{B} > L_{A}$ 29. $The moment of inertia of a body about a given axis is 1.2 kg m^{2} . Initially, the body is at rest. Inorder to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/ sec^{2} must be applied about that axis for a duration of$ (1) $4 s$ (2) $2 s$ (3) $8 s$ (4) $10 s$ 30. $Consider a uniform wire of mass M and length L . It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :$ (1) $\frac{1}{4} \frac{ML ^{2}}{π ^{2}}$ (2) $\frac{2}{5} \frac{ML ^{2}}{π ^{2}}$ (3) $\frac{ML ^{2}}{π ^{2}}$ (4) $\frac{1}{2} \frac{ML ^{2}}{π ^{2}}$