Rotational Mechanics PYQs Set 4 (PDF)

Set 4 of 14 · Questions 91-120 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 4 (Q91-120)
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91. $A rod of linear mass density ' λ' and length ' L' is bent to form a ring of radius ' R '. Moment of inertia of ring about any of its diameter is.$ (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) $\frac{λ L ^{3}}{12}$ 92. $A solid sphere of radius R has its outer half removed, so that its radius becomes (R /2) . Then its moment of inertia about the diameter is$ (1) $becomes \frac{1}{2} of its initial value.$ (2) $is unchanged.$ (3) $becomes \frac{1}{16} of initial value.$ (4) $becomes \frac{1}{32} of initial value.$ 93. $A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?$ (1) $Angular velocity$ (2) $Moment of inertia$ (3) $Rotational kinetic energy$ (4) $Angular momentum$ 94. $A constant torque acting on a uniform circular wheel changes its angular momentum from A_{0} to 4 A_{0} in 4 seconds. The magnitude of the torque is$ (1) $\frac{3 A _{0}}{4}$ (2) $A_{0}$ (3) $4 A_{0}$ (4) $12 A_{o}$ 95. $Two discs of same moment of inertia rotating about their regular axis passing through center and perpendicular to the plane of disc with angular velocities ω_{1} and ω_{2} . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is [NEET 2017]$ (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) $\frac{I}{8} (ω_{1} - ω_{2})^{2}$ 96. $A car of mass m is moving on a level circular track of radius R . If μ_{s} represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by$ (1) $μ_{s} mRg$ (2) $\frac{Rg}{μ _{s}}$ (3) $\frac{mRg}{μ _{s}}$ (4) $μ_{s} Rg$ 97. $A disc has mass ' M' and radius ' R'. How much tangential force should be applied to the rim of the disc so as to rotate with angular velocity^{’} ω^{’} in time ' t ?$ (1) $\frac{MRω}{4 t}$ (2) $\frac{MRω}{2 t}$ (3) $\frac{MRω}{t}$ (4) $MR ω t$ 98. $What is the torque of the force F = 2 i - 3 j + 4 k N acting at the point r = 3 i + 2 j + 3 k m about origin?$ (1) $- 6 i + 6 j - 12 k$ (2) $- 17 i + 6 j + 13 k$ (3) $6 i - 6 j + 12 k$ (4) $17 i - 6 j - 13 k$ 99. $Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If V_{S}, V_{R} and V_{D} are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is$ (1) $V_{S} > V_{R} > V_{D}$ (2) $V_{D} > V_{S} > V_{R}$ (3) $V_{R} > V_{D} > V_{S}$ (4) $V_{S} > V_{D} > V_{R}$ 100. $Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R . They all spin with the same angular speed (f) about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation$ (1) $W_{C} > W_{B} > W_{A}$ (2) $W_{A} > W_{B} > W_{C}$ (3) $W_{B} > W_{A} > W_{C}$ (4) $W_{A} > W_{C} > W_{B}$ 101. $Which of the following type of wheels of same mass and radius will have largest moment of inertia?$ (1) $Ring$ (2) $Angular disc$ (3) $Solid disc$ (4) $Cylindrical disc$ 102. $A body is rolling without slipping on a horizóntal plane. If the rotational kinetic energy of the body 50 % of its total kinetic energy, then the body is$ (1) $Hollow sphere$ (2) $Solid sphere$ (3) $Solid cylinder$ (4) $Thin circular ring$ 103. $The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 s. The angular acceleration in rad / s^{2} is [NEET 2022]$ (1) $4 π$ (2) $12 π$ (3) $104 π$ (4) $2 π$ 104. $A thin circular disc of mass 12 kg and radius 0.5 m rotates with an angular velocity of 100 rad / s . The rotational kinetic energy of the disc is$ (1) $12.2 kJ$ (2) $5.5 kJ$ (3) $9.2 kJ$ (4) $7.5 kJ$ 105. $A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first? [NEET 2016]$ (1) $Sphere$ (2) $Both reach at the same time$ (3) $Depends on their masses$ (4) $Disc$ 106. $A particle performs uniform circular motion with an angular momentum L . If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes$ (1) $2 L$ (2) $4 L$ (3) $\frac{L}{2}$ (4) $\frac{L}{4}$ 107. $If L and P represent the angular momentum and linear momentum respectively of a particle of mass ' m' having position vector as r = a (i cos ωt + j sin ωt) . The direction of force is$ (1) $Opposite to the direction of L$ (2) $Opposite to the direction of L \times P$ (3) $Opposite to the direction of r$ (4) $Opposite to the direction of P$ 108. $Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is = M (\frac{R ^{2}}{4} + \frac{L ^{2}}{12}) . If such a cylinder is to be made for a given mass of a material, the ratio L/R for it to have minimum possible I is:$ (1) $\frac{2}{3}$ (2) $\frac{2}{3}$ (3) $\frac{3}{2}$ (4) $\frac{3}{2}$ 109. $A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ (t) = 5 t^{2} - 8 t, where θ (t) is the angular position of the rotating disc as a function of time t . How much power is delivered by the applied torque, when t = 2 s ?$ (1) $72 MR^{2}$ (2) $8 MR^{2}$ (3) $108 MR^{2}$ (4) $60 MR^{2}$ 110. $Two rotating bodies A and B of masses m and 2 m with moments of inertia I_{A} and I_{B} (I_{B} > I_{A}) have equal kinetic energy of rotation. If L_{A} and L_{B} be their angular momenta respectively, then [NEET 2016]$ (1) $L_{A} = \frac{L _{B}}{2}$ (2) $L_{A} = 2 L_{B}$ (3) $L_{B} > L_{A}$ (4) $L_{A} > L_{B}$ 111. $A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of same thickness and radius but of mass \frac{1}{8} M is placed gently on the first disc coaxially. The angular velocity of the system is now$ (1) $\frac{8}{9} ω$ (2) $\frac{5}{9} ω$ (3) $\frac{1}{3} ω$ (4) $\frac{2}{9} ω$ 112. $A solid sphere is pushed on a horizontal surface such that it slides with a speed 3.5 ms^{- 1} initially without rolling. The sphere will start rolling without slipping when its velocity becomes$ (1) $2.5 ms^{- 1}$ (2) $5 ms^{- 1}$ (3) $3.5 ms^{- 1}$ (4) $7 ms^{- 1}$ 113. $Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:-$ (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) $The cylinder has the greatest and the sphere has the least velocity of the entre of mass at the bottom of the inclined plane.$ 114. $A disc of radius R and thickness R /6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is$ (1) $\frac{I}{5}$ (2) $\frac{I}{6}$ (3) $\frac{I}{32}$ (4) $\frac{1}{64}$ 115. $The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R < L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :$ (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) $\frac{3}{8} M R^{2} + \frac{7}{12} M L^{2}$ 116. $A wheel is rotating freely with an angular speed on a shaft. The moment of inertia of the wheel is 1 and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is$ (1) $\frac{5}{6}$ (2) $\frac{1}{4}$ (3) $0$ (4) $\frac{3}{4}$ 117. $The moment of inertia of a rigid body about an axis$ (1) $does not depend on its mass$ (2) $does not depend on its shape$ (3) $depends on the position of axis of rotation$ (4) $does not depend on its size$ 118. $A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distant from the hinges for opening or closing the door is$ (1) $1.2 N$ (2) $3.6 N$ (3) $2.4 N$ (4) $4 N$ 119. $Three bodies a ring (R), a solid cylinder (C) and a solid sphere (S) having same mass and same radius roll down the inclined plane without slipping. They start from rest, if v_{R}, v_{C} and v_{S} are velocities of respective bodies on reaching the bottom of the plane, then$ (1) $v_{R} = v_{C} = v_{S}$ (2) $v_{R} > v_{C} > v_{S}$ (3) $v_{R} < v_{C} < v_{S}$ (4) $v_{R} = v_{C} > v_{S}$ 120. $A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm^{2} and radius 10 cm . The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N . The angular velocity of the wheel after 10 s is x rad / s, where x is______$