Rotational Mechanics PYQs Set 4 (PDF)

Set 4 of 12 · Questions 91-120 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 4 (Q91-120)
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91. $A body is rolling without slipping on a horizóntal plane. If the rotational kinetic energy of the body 50 % of its total kinetic energy, then the body is$ (1) $Hollow sphere$ (2) $Solid sphere$ (3) $Solid cylinder$ (4) $Thin circular ring$ 92. $The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 s. The angular acceleration in rad / s^{2} is [NEET 2022]$ (1) $4 π$ (2) $12 π$ (3) $104 π$ (4) $2 π$ 93. $A thin circular disc of mass 12 kg and radius 0.5 m rotates with an angular velocity of 100 rad / s . The rotational kinetic energy of the disc is$ (1) $12.2 kJ$ (2) $5.5 kJ$ (3) $9.2 kJ$ (4) $7.5 kJ$ 94. $A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first? [NEET 2016]$ (1) $Sphere$ (2) $Both reach at the same time$ (3) $Depends on their masses$ (4) $Disc$ 95. $A particle performs uniform circular motion with an angular momentum L . If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes$ (1) $2 L$ (2) $4 L$ (3) $\frac{L}{2}$ (4) $\frac{L}{4}$ 96. $If L and P represent the angular momentum and linear momentum respectively of a particle of mass ' m' having position vector as r = a (i cos ωt + j sin ωt) . The direction of force is$ (1) $Opposite to the direction of L$ (2) $Opposite to the direction of L \times P$ (3) $Opposite to the direction of r$ (4) $Opposite to the direction of P$ 97. $Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is = M (\frac{R ^{2}}{4} + \frac{L ^{2}}{12}) . If such a cylinder is to be made for a given mass of a material, the ratio L/R for it to have minimum possible I is:$ (1) $\frac{2}{3}$ (2) $\frac{2}{3}$ (3) $\frac{3}{2}$ (4) $\frac{3}{2}$ 98. $A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ (t) = 5 t^{2} - 8 t, where θ (t) is the angular position of the rotating disc as a function of time t . How much power is delivered by the applied torque, when t = 2 s ?$ (1) $72 MR^{2}$ (2) $8 MR^{2}$ (3) $108 MR^{2}$ (4) $60 MR^{2}$ 99. $Two rotating bodies A and B of masses m and 2 m with moments of inertia I_{A} and I_{B} (I_{B} > I_{A}) have equal kinetic energy of rotation. If L_{A} and L_{B} be their angular momenta respectively, then [NEET 2016]$ (1) $L_{A} = \frac{L _{B}}{2}$ (2) $L_{A} = 2 L_{B}$ (3) $L_{B} > L_{A}$ (4) $L_{A} > L_{B}$ 100. $A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of same thickness and radius but of mass \frac{1}{8} M is placed gently on the first disc coaxially. The angular velocity of the system is now$ (1) $\frac{8}{9} ω$ (2) $\frac{5}{9} ω$ (3) $\frac{1}{3} ω$ (4) $\frac{2}{9} ω$ 101. $A solid sphere is pushed on a horizontal surface such that it slides with a speed 3.5 ms^{- 1} initially without rolling. The sphere will start rolling without slipping when its velocity becomes$ (1) $2.5 ms^{- 1}$ (2) $5 ms^{- 1}$ (3) $3.5 ms^{- 1}$ (4) $7 ms^{- 1}$ 102. $Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:-$ (1) $The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.$ (2) $The ring has the greatest and the cylinder has the least velocity of the centre f mass at the bottom of the inclined plane.$ (3) $All of them will have same velocity.$ (4) $The cylinder has the greatest and the sphere has the least velocity of the entre of mass at the bottom of the inclined plane.$ 103. $A disc of radius R and thickness R /6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is$ (1) $\frac{I}{5}$ (2) $\frac{I}{6}$ (3) $\frac{I}{32}$ (4) $\frac{1}{64}$ 104. $The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R < L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :$ (1) $\frac{3}{4} M R^{2} + \frac{7}{12} M L^{2}$ (2) $\frac{3}{8} M R^{2} + \frac{1}{6} M L^{2}$ (3) $\frac{3}{4} M R^{2} + \frac{1}{6} M L^{2}$ (4) $\frac{3}{8} M R^{2} + \frac{7}{12} M L^{2}$ 105. $A wheel is rotating freely with an angular speed on a shaft. The moment of inertia of the wheel is 1 and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is$ (1) $\frac{5}{6}$ (2) $\frac{1}{4}$ (3) $0$ (4) $\frac{3}{4}$ 106. $The moment of inertia of a rigid body about an axis$ (1) $does not depend on its mass$ (2) $does not depend on its shape$ (3) $depends on the position of axis of rotation$ (4) $does not depend on its size$ 107. $A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distant from the hinges for opening or closing the door is$ (1) $1.2 N$ (2) $3.6 N$ (3) $2.4 N$ (4) $4 N$ 108. $Three bodies a ring (R), a solid cylinder (C) and a solid sphere (S) having same mass and same radius roll down the inclined plane without slipping. They start from rest, if v_{R}, v_{C} and v_{S} are velocities of respective bodies on reaching the bottom of the plane, then$ (1) $v_{R} = v_{C} = v_{S}$ (2) $v_{R} > v_{C} > v_{S}$ (3) $v_{R} < v_{C} < v_{S}$ (4) $v_{R} = v_{C} > v_{S}$ 109. $Which of the following are correct expression for torque acting on a body? (A0 τ=r\timesL(B) τ = \frac{d}{dt} (r \times p) (C) τ = r \times \frac{d p}{dt} (D) τ=Iα(E.)τ=r\timesF(r = position vector; p = linear momentum; L = angular momentum; α = angularacceleration; I = moment of inertia; F = force; t = time) Choose the correct answer from the options given below:$ (1) $A, B, D and E Only$ (2) $C and D Only$ (3) $B, C, D and E Only$ (4) $B, D and E Only$ 110. $A body of mass 5 kg acquires an acceleration of 10 rad s^{- 2} due to an applied torque of 2 Nm . Its radius of gyrations is$ (1) $2.5 m$ (2) $2.5 m$ (3) $0.2 m$ (4) $0.2 m$ 111. $Let M be the mass and L be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is$ (1) $1$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $\frac{1}{8}$ 112. $A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder ' a_{c}' to that of sphere ' a_{s}' is$ (1) $\frac{11}{15}$ (2) $\frac{13}{14}$ (3) $\frac{15}{14}$ (4) $\frac{14}{15}$ 113. $When the position vector r = x i + y j + z k changes sign as - r, which one of the following vector will not flip under sign change ?$ (1) $Angular momentum$ (2) $Velocity$ (3) $Acceleration$ (4) $Linear momentum$ 114. $A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_{t}) as well as rotational kinetic energy (K_{r}) simultaneously. The ratio K_{t} : (K_{t} + K_{r}) for the sphere is [NEET 2018]$ (1) $10 : 7$ (2) $5 : 7$ (3) $7 : 10$ (4) $2 : 5$ 115. $A uniform disc of mass 100 kg and radius 2 m is rotating at 1 rad / s about a perpendicular axis passing through its centre. A boy of mass 60 kg standing at the centre of the disk suddenly jumps to a point which is 1 m from the centre of the disc. The final angular velocity of the boy (in rad/s) is$ (1) $0.77$ (2) $0.5$ (3) $41$ (4) $2$ 116. $Moment of inertia of a body about a given axis is 1.5 kg m^{2} . Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad / s^{2} must be applied about the axis for a duration of:$ (1) $2.5 s$ (2) $2 s$ (3) $5 s$ (4) $3 s$ 117. $The angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration of the motor wheel is$ (1) $6 π rad / s^{2}$ (2) $2 π rad / s^{2}$ (3) $8 π rad / s^{2}$ (4) $4 π rad / s^{2}$ 118. $A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its center of mass has speed of 20 cm / s . How much work is needed to stop it? [NEET 2019]$ (1) $30 KJ$ (2) $2 J$ (3) $1 J$ (4) $3 J$ 119. $A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2 π revolutions is [NEET 2019]$ (1) $2 \times 10^{- 3} N - m$ (2) $12 \times 10^{- 4} N - m$ (3) $2 \times 10^{6} N - m$ (4) $2 \times 10^{- 6} N - m$ 120. $A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia% out the axle is 200 kg m^{2} . It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s^{- 1} relative to the ground. Time taken by the man to complete one revolution is$ (1) $πs$ (2) $\frac{3 π}{2} s$ (3) $2 πs$ (4) $\frac{π}{2} s$