Rotational Mechanics PYQs Set 2 (PDF)

Set 2 of 12 · Questions 31-60 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 2 (Q31-60)
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31. $From a circular disc of radius R and mass 9 M, a small disc of mass M and radius R /3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is$ (1) $\frac{40}{9} M R^{2}$ (2) $M R^{2}$ (3) $4 M R^{2}$ (4) $\frac{4}{9} M R^{2}$ 32. $A body rotating with uniform acceleration about its geometrical axis makes 8 rotations in the first 2 seconds. The number of rotations the body makes in the next 3 seconds is(Initially the body is at rest)$ (1) $50$ (2) $25$ (3) $42$ (4) $21$ 33. $The ratio of the radii of two solid spheres of same mass is 2 : 3 . The ratio of the moments of inertia of the spheres about their diameters is$ (1) $4:9$ (2) $2 : 3$ (3) $8 : 27$ (4) $16 : 81$ 34. $The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians):$ (1) $\frac{π}{6}$ (2) $\frac{π}{3}$ (3) $\frac{π}{8}$ (4) $\frac{π}{4}$ 35. $The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is [NEET 2023]$ (1) $5 : 3$ (2) $2 : 5$ (3) $5 : 2$ (4) $3 : 5$ 36. $A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm . The moment of inertia of this pair of spheres about the tangent passing through the point of contact is____kg . m^{2} .$ (1) $0.72$ (2) $0.36$ (3) $0.18$ (4) $0.63$ 37. $If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is$ (1) $1 : 8$ (2) $2 : 5$ (3) $2 : 3$ (4) $1 : 4$ 38. $The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'Ι(x)'. Which one of the graphs represents the variation of Ι(x) with x correctly ?$ (1) (2) (3) (4) 39. $Consider a wheel rotating around a fixed axis. If the rotation angle θ varies with time as θ = a t^{2}, then the total acceleration of a point A on the rim of the wheel is (v being the tangential velocity)$ (1) $\frac{v}{t} 1 + 4 a^{2} t^{4}$ (2) $\frac{v}{t}$ (3) $\frac{v}{t} (1 + 4 a^{2} t^{4})$ (4) $(1 + 4 a^{2} t^{4})$ 40. $Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is I . If the same rod is bent into a ring and its moment of inertia about its diameter is I^{’}, then the ratio \frac{I}{I ^{’}} is$ (1) $\frac{8}{3} π^{2}$ (2) $\frac{5}{3} π^{2}$ (3) $\frac{3}{2} π^{2}$ (4) $\frac{2}{3} π^{2}$ 41. $A disc of moment of inertia I_{1} is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed ω_{1} . Another disc of moment of inertia I_{2} having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed ω_{2} . The energy lost by the initial rotating disc is$ (1) $\frac{1}{2} (\frac{I _{1} + I _{2}}{I _{1} I _{2}}) ω_{1}^{2}$ (2) $\frac{1}{2} (\frac{I _{1} I _{2}}{I _{1} - I _{2}}) ω_{1}^{2}$ (3) $\frac{1}{2} (\frac{I _{1} - I _{2}}{I _{1} I _{2}}) ω_{1}^{2}$ (4) $\frac{1}{2} (\frac{I _{1} I _{2}}{I _{1} + I _{2}}) ω_{1}^{2}$ 42. $The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle 6 without slipping and slipping down the incline without rolling is$ (1) $5 : 7$ (2) $2 : 3$ (3) $2 : 5$ (4) $7 : 5$ 43. $The moment of the force, F = 4 i + 5 j - 6 k at (2, 0, - 3), about the point (2, - 2, - 2), is given by [NEET 2018]$ (1) $- 7 i - 8 j - 4 k$ (2) $- 4 i - j - 8 k$ (3) $- 8 i - 4 j - 7 k$ (4) $- 7 i - 4 j - 8 k$ 44. $A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_{t}) as well as rotational kinetic energy (K_{r}) simultaneously. The ratio K_{t} : (K_{t} + K_{r}) for the sphere is$ (1) $7: 10$ (2) $5: 7$ (3) $10: 7$ (4) $2: 5$ 45. $The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is ' I (x)^{’}'. Which one of the graphs represents the variation of I (x) with x correctly?$ (1) (2) (3) (4) 46. $The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is:$ (1) $\frac{3}{8} Mr^{2}$ (2) $2 Mr^{2}$ (3) $1 2 Mr^{2}$ (4) $3 2 Mr^{2}$ 47. $A solid sphere rolls without slipping on an inclined plane at an angle θ . The ratio of total kinetic energ? to its rotational kinetic energy is$ (1) $\frac{7}{2}$ (2) $\frac{5}{2}$ (3) $\frac{7}{3}$ (4) $\frac{5}{4}$ 48. $A spherical bob of mass 250 g is attached to the end of a string having length 50 cm . The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is 72 N . The maximum possible value of angular velocity of bob (in rad / s) is$ (1) $18$ (2) $24$ (3) $28$ (4) $32$ 49. $A force F = α i + 3 j + 6 k is acting at a point r = 2 i - 6 j - 12 k . The value of α for which angular momentum about origin is conserved is$ (1) $zero$ (2) $1$ (3) $- 1$ (4) $2$ 50. $A wheel of moment of inertia 2 kg m^{2} is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad / s . Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is$ (1) $24 kg m^{2} / s$ (2) $72 kg m^{2} / s$ (3) $48 kg m^{2} / s$ (4) $96 kg m^{2} / s$ 51. $A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (E_{sphere} / E_{cylinder}) will be$ (1) $2 : 3$ (2) $1 : 5$ (3) $1 : 4$ (4) $3 : 1$ 52. $The moment of inertia of a rectangular plate of mass M, length L and breadth B, about an axis passing through its centre and perpendicular to its plane is$ (1) $\frac{M ( L + B )}{12}$ (2) $\frac{M ( L ^{2} )}{12}$ (3) $\frac{M ( L ^{2} + B ^{2} )}{12}$ (4) $\frac{M ( B _{2} )}{12}$ 53. $A body having a moment of inertia about its axis of rotation equal to 3 kg m^{2} is rotating with angular velocity of 3 rad s^{- 1} . Kinetic energy of this rotating body is same as that of a body of mass 27 kg moving with velocity v . The value of v is$ (1) $2 m s^{- 1}$ (2) $1 m s^{- 1}$ (3) $1.5 m s^{- 1}$ (4) $0.5 m s^{- 1}$ 54. $A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω . Two particleshaving mass m each are now attached at diametrically opposite points. The angular speed of the ring will become:$ (1) $ω \frac{M}{M + m}$ (2) $ω \frac{M + 2 m}{M}$ (3) $ω \frac{M}{M + 2 m}$ (4) $ω \frac{M - 2 m}{M + 2 m}$ 55. $Assertion (A) : Angular speed, linear speed and kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun. Reason (R) : Angular momentum is constant as no torque acts on the planet.$ (1) $Both A and R are true and R is a correct explanation for A .$ (2) $Both A and R are true but R is not a correct explanation for A.$ (3) $A is true, R is false.$ (4) $A is false, R is true.$ 56. $The angular momentum of a wheel having a rotational inertia of 0.2 kg m^{2} about its symmetric axis decreases from 4 to 2 kg m^{2} s^{- 1} in 4 s . The average power of the wheel is$ (1) $7.5 W$ (2) $15 W$ (3) $5 W$ (4) $12 W$ 57. $Two particles of masses m1, m2 move with initial velocities u1 and u2 . On collision, one of the particles get excited to higher level, after absorbing energy ε If final velocities of particles be v1 and v2 then we must have:$ (1) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} - ε$ (2) $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} - ε = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$ (3) $\frac{1}{2} m_{1}^{2} u_{1}^{2} + \frac{1}{2} m_{2}^{2} u_{2}^{2} + ε = \frac{1}{2} m_{1}^{2} v_{1}^{2} + \frac{1}{2} m_{2}^{2} v_{2}^{2}$ (4) $m_{1}^{2} u_{1} + m_{2}^{2} u_{2} - ε = m_{1}^{2} v_{1} + m_{2}^{2} v_{2}$ 58. $A wheel of mass 20 kg and radius 30 cm is rotating at an angular speed of 80 rev / min when the motor is turned off. Neglecting the friction at the axis, calculate the force that must be applied tangentially to the wheel to bring it to rest in 5 rev.$ (1) $1.06 π N$ (2) $2.06 π N$ (3) $3.06 π N$ (4) $4.06 π N$ 59. $A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with$ (1) $aluminium at interior and iron surround to it$ (2) $iron at interior and aluminium surround to it$ (3) $using iron and aluminium layers in alternate order$ (4) $sheet of iron is used at both external surface and aluminium sheet as internal layers.$ 60. $A wheel having moment of inertia 2kg m^{2} about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in one minute would be$ (1) $\frac{2 π}{15} Nm$ (2) $\frac{π}{12} Nm$ (3) $\frac{π}{15} Nm$ (4) $\frac{π}{18} Nm$