Rotational Mechanics PYQs Set 3 (PDF)

Set 3 of 14 · Questions 61-90 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 3 (Q61-90)
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61. $Assertion (A) : Angular speed, linear speed and kinetic energy change with time but angular momentum remains constant for a planet orbiting the sun. Reason (R) : Angular momentum is constant as no torque acts on the planet.$ (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) $A is false, R is true.$ 62. $The angular momentum of a wheel having a rotational inertia of 0.2 kg m^{2} about its symmetric axis decreases from 4 to 2 kg m^{2} s^{- 1} in 4 s . The average power of the wheel is$ (1) $7.5 W$ (2) $15 W$ (3) $5 W$ (4) $12 W$ 63. $Two particles of masses m1, m2 move with initial velocities u1 and u2 . On collision, one of the particles get excited to higher level, after absorbing energy ε If final velocities of particles be v1 and v2 then we must have:$ (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) $m_{1}^{2} u_{1} + m_{2}^{2} u_{2} - ε = m_{1}^{2} v_{1} + m_{2}^{2} v_{2}$ 64. $A wheel of mass 20 kg and radius 30 cm is rotating at an angular speed of 80 rev / min when the motor is turned off. Neglecting the friction at the axis, calculate the force that must be applied tangentially to the wheel to bring it to rest in 5 rev.$ (1) $1.06 π N$ (2) $2.06 π N$ (3) $3.06 π N$ (4) $4.06 π N$ 65. $A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with$ (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) $sheet of iron is used at both external surface and aluminium sheet as internal layers.$ 66. $A wheel having moment of inertia 2kg m^{2} about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel’s rotation in one minute would be$ (1) $\frac{2 π}{15} Nm$ (2) $\frac{π}{12} Nm$ (3) $\frac{π}{15} Nm$ (4) $\frac{π}{18} Nm$ 67. $A round disc of moment of inertia I_{2} about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I_{1} rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is$ (1) $\frac{I _{2} ω}{l _{1} + l _{2}}$ (2) $ω$ (3) $\frac{I _{1} ω}{I _{1} + I _{2}}$ (4) $\frac{( I _{1} + I _{2} ) ω}{I _{1}}$ 68. $The angular momentum of a solid cylinder rotating about its geometric axis with angular speed 40 rad s^{- 1} is 2 kg m^{2} s^{- 1} . If the radius of the cylinder is 10 cm, the mass of the cylinder is$ (1) $2 kg$ (2) $5 kg$ (3) $8 kg$ (4) $10 kg$ 69. $An electric motor drill, rated 350 W has an efficiency of 35 % . The torque produced, if it is working at 3000 rpm is$ (1) $0.25 N m$ (2) $0.35 N m$ (3) $0.39 N m$ (4) $0.30 N m$ 70. $A flywheel is rotating at a rate of 150 rev / minute . If it slows at constant retardation of π rads^{- 2}, then the time required for the wheel to come to rest is$ (1) $2.5 s$ (2) $5 s$ (3) $4 s$ (4) $6 s$ 71. $A body is located at (1, 1, 1) m and experiences a force of 2 N in the direction i + j . The torque acting on the body in N - m is$ (1) $(- 2 i + 2 j)$ (2) $(- i + j)$ (3) $(i - j)$ (4) $(2 i + 2 j)$ 72. $The linear mass density of a thin rod AB of length L varies from A to B as ⋋ (x) = ⋋_{0} (1 + \frac{x}{L}), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:$ (1) $\frac{2}{5} M L^{2}$ (2) $\frac{5}{12} M L^{2}$ (3) $\frac{3}{7} M L^{2}$ (4) $\frac{7}{18} M L^{2}$ 73. $The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc$ (1) $\frac{1}{2} M R^{2}$ (2) $M R^{2}$ (3) $\frac{2}{5} M R^{2}$ (4) $\frac{3}{2} M R^{2}$ 74. $A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :$ (1) $Solid sphere$ (2) $Solid cylinder$ (3) $Hollow cylinder$ (4) $Ring$ 75. $An automobile moves on a road with a speed of 54 km h^{- 1} . The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m^{2} . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is$ (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) $8.58 kg m^{2} s^{- 2}$ 76. $A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω . Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be$ (1) $\frac{Mω}{4 m}$ (2) $\frac{Mω}{M + 4 m}$ (3) $\frac{( M + 4 m ) ω}{M}$ (4) $\frac{( M - 4 m ) ω}{M + 4 m}$ 77. $The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel to its diameter is$ (1) $\frac{5}{4} M R^{2}$ (2) $\frac{2}{3} M R^{2}$ (3) $\frac{3}{2} M R^{2}$ (4) $\frac{4}{5} M R^{2}$ 78. $A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by$ (1) $\frac{( M + 2 m ) ω}{2 m}$ (2) $\frac{2 Mω}{M + 2 m}$ (3) $\frac{( M + 2 m ) ω}{M}$ (4) $\frac{Mω}{M + 2 m}$ 79. $If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by$ (1) $7: 10$ (2) $2: 5$ (3) $10 : 7$ (4) $5 : 7$ 80. $A ballet dancer suddenly folds her outstretched arms. Her angular velocity$ (1) $increases$ (2) $decreases$ (3) $remains the same$ (4) $may increase or decrease$ 81. $The angular speed of a rigid body rotating about a fixed axis is (8 - 2 t) rad s^{- 1} . The angle through which the body rotates before it comes to rest is$ (1) $8 rad$ (2) $12 rad$ (3) $. 16 rad$ (4) $20 rad$ 82. $A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere? [NEET 2018]$ (1) $Rotational kinetic energy$ (2) $Moment of inertia$ (3) $Angular velocity$ (4) $Angular momentum$ 83. $The ratio of the radius of gyration of a thin uniform disc about an axis passing through its center and normal to its plane to the radius of gyration of the disc about its diameter is [NEET 2022]$ (1) $2 : 1$ (2) $4 : 1$ (3) $1 : 2$ (4) $2 : 1$ 84. $A rigid body is rotating with angular velocity ω about an axis of rotation. Let v be the linear velocity of particle which is at perpendicular distance r from the axis of rotation. Then the relation v = rω implies that$ (1) $ω does not depend on r$ (2) $ω \propto \frac{1}{r}$ (3) $ω = r$ (4) $ω = 0$ 85. $A force F = α i^+ 3 j^+ 6 k^is acting at a point r = 2 i^-6 j^-12 k^. The value of α for which angular momentum about origin is conserved is :$ (1) $2$ (2) $zero$ (3) $1$ (4) $-1$ 86. $A body of mass 5 kg moving with a uniform speed 32 ms^{- 1} in X - Y plane along the line y = x + 4 . The angular momentum of the particle about the origin will be______kgm^{2} s^{- 1} .$ 87. $A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is____J . (g = 10 m / s^{2})$ 88. $Two discs of moment of inertia I_{1} = 4 kg m^{2} and I_{2} = 2 kg m^{2} about their central axes ∖ & normal to their planes, rotating with angular speeds 10 rad / s ∖ & 4 rad / s respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is_____ J.$ 89. $A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800rpm in 10sec. The number of rotations made in the process is$ 90. $A circular disc reaches from top to bottom of an inclined plane of length l . When it slips down the plane, if takes t s . When it rolls down the plane then it takes (\frac{α}{2})^{1/2} t s, where α is______$