Rotational Mechanics PYQs Set 3 (PDF)

Set 3 of 12 · Questions 61-90 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 3 (Q61-90)
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61. $A round disc of moment of inertia I_{2} about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I_{1} rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is$ (1) $\frac{I _{2} ω}{l _{1} + l _{2}}$ (2) $ω$ (3) $\frac{I _{1} ω}{I _{1} + I _{2}}$ (4) $\frac{( I _{1} + I _{2} ) ω}{I _{1}}$ 62. $The angular momentum of a solid cylinder rotating about its geometric axis with angular speed 40 rad s^{- 1} is 2 kg m^{2} s^{- 1} . If the radius of the cylinder is 10 cm, the mass of the cylinder is$ (1) $2 kg$ (2) $5 kg$ (3) $8 kg$ (4) $10 kg$ 63. $An electric motor drill, rated 350 W has an efficiency of 35 % . The torque produced, if it is working at 3000 rpm is$ (1) $0.25 N m$ (2) $0.35 N m$ (3) $0.39 N m$ (4) $0.30 N m$ 64. $A flywheel is rotating at a rate of 150 rev / minute . If it slows at constant retardation of π rads^{- 2}, then the time required for the wheel to come to rest is$ (1) $2.5 s$ (2) $5 s$ (3) $4 s$ (4) $6 s$ 65. $A body is located at (1, 1, 1) m and experiences a force of 2 N in the direction i + j . The torque acting on the body in N - m is$ (1) $(- 2 i + 2 j)$ (2) $(- i + j)$ (3) $(i - j)$ (4) $(2 i + 2 j)$ 66. $The linear mass density of a thin rod AB of length L varies from A to B as ⋋ (x) = ⋋_{0} (1 + \frac{x}{L}), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:$ (1) $\frac{2}{5} M L^{2}$ (2) $\frac{5}{12} M L^{2}$ (3) $\frac{3}{7} M L^{2}$ (4) $\frac{7}{18} M L^{2}$ 67. $The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc$ (1) $\frac{1}{2} M R^{2}$ (2) $M R^{2}$ (3) $\frac{2}{5} M R^{2}$ (4) $\frac{3}{2} M R^{2}$ 68. $A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :$ (1) $Solid sphere$ (2) $Solid cylinder$ (3) $Hollow cylinder$ (4) $Ring$ 69. $An automobile moves on a road with a speed of 54 km h^{- 1} . The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m^{2} . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is$ (1) $10.86 kg m^{2} s^{- 2}$ (2) $2.86 kg m^{2} s^{- 2}$ (3) $6.66 kg m^{2} s^{- 2}$ (4) $8.58 kg m^{2} s^{- 2}$ 70. $A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω . Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be$ (1) $\frac{Mω}{4 m}$ (2) $\frac{Mω}{M + 4 m}$ (3) $\frac{( M + 4 m ) ω}{M}$ (4) $\frac{( M - 4 m ) ω}{M + 4 m}$ 71. $The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel to its diameter is$ (1) $\frac{5}{4} M R^{2}$ (2) $\frac{2}{3} M R^{2}$ (3) $\frac{3}{2} M R^{2}$ (4) $\frac{4}{5} M R^{2}$ 72. $A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by$ (1) $\frac{( M + 2 m ) ω}{2 m}$ (2) $\frac{2 Mω}{M + 2 m}$ (3) $\frac{( M + 2 m ) ω}{M}$ (4) $\frac{Mω}{M + 2 m}$ 73. $If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by$ (1) $7: 10$ (2) $2: 5$ (3) $10 : 7$ (4) $5 : 7$ 74. $A ballet dancer suddenly folds her outstretched arms. Her angular velocity$ (1) $increases$ (2) $decreases$ (3) $remains the same$ (4) $may increase or decrease$ 75. $The angular speed of a rigid body rotating about a fixed axis is (8 - 2 t) rad s^{- 1} . The angle through which the body rotates before it comes to rest is$ (1) $8 rad$ (2) $12 rad$ (3) $. 16 rad$ (4) $20 rad$ 76. $A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere? [NEET 2018]$ (1) $Rotational kinetic energy$ (2) $Moment of inertia$ (3) $Angular velocity$ (4) $Angular momentum$ 77. $The ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is [NEET 2022]$ (1) $2 : 1$ (2) $4 : 1$ (3) $1 : 2$ (4) $2 : 1$ 78. $A rigid body is rotating with angular velocity ω about an axis of rotation. Let v be the linear velocity of particle which is at perpendicular distance r from the axis of rotation. Then the relation v = rω implies that$ (1) $ω does not depend on r$ (2) $ω \propto \frac{1}{r}$ (3) $ω = r$ (4) $ω = 0$ 79. $A force F = α i^+ 3 j^+ 6 k^is acting at a point r = 2 i^-6 j^-12 k^. The value of α for which angular momentum about origin is conserved is :$ (1) $2$ (2) $zero$ (3) $1$ (4) $-1$ 80. $A rod of linear mass density ' λ' and length ' L' is bent to form a ring of radius ' R '. Moment of inertia of ring about any of its diameter is.$ (1) $\frac{λ L ^{3}}{8 π ^{2}}$ (2) $\frac{λ L ^{3}}{16 π ^{2}}$ (3) $\frac{λ L ^{3}}{4 π ^{2}}$ (4) $\frac{λ L ^{3}}{12}$ 81. $A solid sphere of radius R has its outer half removed, so that its radius becomes (R /2) . Then its moment of inertia about the diameter is$ (1) $becomes \frac{1}{2} of its initial value.$ (2) $is unchanged.$ (3) $becomes \frac{1}{16} of initial value.$ (4) $becomes \frac{1}{32} of initial value.$ 82. $A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?$ (1) $Angular velocity$ (2) $Moment of inertia$ (3) $Rotational kinetic energy$ (4) $Angular momentum$ 83. $A constant torque acting on a uniform circular wheel changes its angular momentum from A_{0} to 4 A_{0} in 4 seconds. The magnitude of the torque is$ (1) $\frac{3 A _{0}}{4}$ (2) $A_{0}$ (3) $4 A_{0}$ (4) $12 A_{o}$ 84. $Two discs of same moment of inertia rotating about their regular axis passing through center and perpendicular to the plane of disc with angular velocities ω_{1} and ω_{2} . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is [NEET 2017]$ (1) $\frac{1}{2} I (ω_{1} + ω_{2})^{2}$ (2) $\frac{1}{4} I (ω_{1} - ω_{2})^{2}$ (3) $I (ω_{1} - ω_{2})^{2}$ (4) $\frac{I}{8} (ω_{1} - ω_{2})^{2}$ 85. $A car of mass m is moving on a level circular track of radius R . If μ_{s} represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by$ (1) $μ_{s} mRg$ (2) $\frac{Rg}{μ _{s}}$ (3) $\frac{mRg}{μ _{s}}$ (4) $μ_{s} Rg$ 86. $A disc has mass ' M' and radius ' R'. How much tangential force should be applied to the rim of the disc so as to rotate with angular velocity^{’} ω^{’} in time ' t ?$ (1) $\frac{MRω}{4 t}$ (2) $\frac{MRω}{2 t}$ (3) $\frac{MRω}{t}$ (4) $MR ω t$ 87. $What is the torque of the force F = 2 i - 3 j + 4 k N acting at the point r = 3 i + 2 j + 3 k m about origin?$ (1) $- 6 i + 6 j - 12 k$ (2) $- 17 i + 6 j + 13 k$ (3) $6 i - 6 j + 12 k$ (4) $17 i - 6 j - 13 k$ 88. $Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If V_{S}, V_{R} and V_{D} are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is$ (1) $V_{S} > V_{R} > V_{D}$ (2) $V_{D} > V_{S} > V_{R}$ (3) $V_{R} > V_{D} > V_{S}$ (4) $V_{S} > V_{D} > V_{R}$ 89. $Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R . They all spin with the same angular speed (f) about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation$ (1) $W_{C} > W_{B} > W_{A}$ (2) $W_{A} > W_{B} > W_{C}$ (3) $W_{B} > W_{A} > W_{C}$ (4) $W_{A} > W_{C} > W_{B}$ 90. $Which of the following type of wheels of same mass and radius will have largest moment of inertia?$ (1) $Ring$ (2) $Angular disc$ (3) $Solid disc$ (4) $Cylindrical disc$