Rotational Mechanics Questions

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Questions 1 of 25

Question:A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

Answers Choices:

\(\frac{{2R}}{{\sqrt {15} }}\)

\(R\sqrt {\frac{2}{{15}}} \)

\(\frac{{4R}}{{\sqrt {15} }}\)

\(\frac{R}{4}\)

Questions 2 of 25

Question:In the figure shown, a cubical block is held stationary against a rough wall by applying force 'F' then incorrect statement among the following is

Answers Choices:

frictional force, f = Mg

F = N, N is normal reaction

F does not apply any torque about centre of mass

N does not apply any torque about centre of mass

Questions 3 of 25

Question:A circular disc of radius R/3 is cut from a circular disc of radius R and mass 9 M as shown. Then moment of inertia of remaining disc about 'O' perpendicular to the plane of the disc is

Answers Choices:

4\({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

9\({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

\(\frac{{37}}{9}{\rm{M}}{{\rm{R}}^{\rm{2}}}\)

\(\frac{{40}}{9}{\rm{M}}{{\rm{R}}^{\rm{2}}}\)

Questions 4 of 25

Question:A particle is confined to rotate in a circular path with decreasing linear speed, then which of the following is correct?

Answers Choices:

L (angular momentum) is conserved about the centre.

only direction of angular momentumL is conserved.

It spirals towards the centre.

its acceleration is towards the centre.

Questions 5 of 25

Question:A disc is rolling without slipping with angular velocity \(\omega \). P and Q are two points equidistant from the centre C. The order of magnitude of velocity is

Answers Choices:

\({v_Q} > {v_C} > {v_P}\)

\({v_P} > {v_C} > {v_Q}\)

\({v_P} = {v_C},{v_Q} = {v_C}/2\)

\({v_P} < {v_C} > {v_Q}\)

Questions 6 of 25

Question:A horizontal circular plate is rotating about a vertical axis passing through its centre with an angular velocity \({\omega _0}\). A man sitting at the centre having two blocks in his hands stretches out his hands so that the moment of inertia of the system doubles. If the kinetic energy of the system is K initially, its final kinetic energy will be

Answers Choices:

2K

K/2

K

K/4

Questions 7 of 25

Question:Two particles each of mass M, are connected by a rigid rod of negligible mass and length L. The system is lying on a horizontal frictionless surface. An impulse Mv, perpendicular to the rod, is given at one end of the rod as shown in the figure: The angular velocity acquired by the rod is

Answers Choices:

4v/L

2v/L

v/L

v/4L

Questions 8 of 25

Question:A particle is in uniform circular motion in a horizontal plane. Its angular momentum is constant when the origin is taken at

Answers Choices:

centre of the circle

any point on the circumference of the circle.

any point inside the circle.

any point outside the circle.

Questions 9 of 25

Question:A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity \({\omega _0}\). When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform \(\omega \)(t) will vary with time t as

Answers Choices:

Questions 10 of 25

Question:A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are

Answers Choices:

up the incline while ascending and down the incline descending.

up the incline while ascending as well as descending.

down the incline while ascending and up the incline while descending.

down the incline while ascending as well as descending.

Questions 11 of 25

Question:One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

Answers Choices:

(1/2)\({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

(1/4) \({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

(1/8) \({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

\(\sqrt 2 \) \({\rm{M}}{{\rm{R}}^{\rm{2}}}\)

Questions 12 of 25

Question:An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

Answers Choices:

angular velocity and total energy (kinetic and potential)

total angular momentum and total energy.

angular velocity and moment of inertia about the axis of rotation.

total angular momentum and moment of inertia about the axis of rotation.

Questions 13 of 25

Question:A thin wire of length L and uniform linear mass density p is bent into a circular loop with centre at O as shown in the figure. The moment of inertia of the loop about the axis XX'is

Answers Choices:

\(\frac{{\rho {L^3}}}{{8{\pi ^2}}}\)

\(\frac{{\rho {L^3}}}{{16{\pi ^2}}}\)

\(\frac{{5\rho {L^3}}}{{16{\pi ^2}}}\)

\(\frac{{3\rho {L^3}}}{{8{\pi ^2}}}\)

Questions 14 of 25

Question:A smooth sphere A is moving on a frictionless horizontal plane with angular speed \(\omega \) and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are \({\omega _A}\) and \({\omega _B}\), respectively. Then

Answers Choices:

\({\omega _A} < {\omega _B}\)

\({\omega _A} = {\omega _B}\)

\({\omega _A} = \omega \)

\({\omega _B} < \omega \)

Questions 15 of 25

Question:Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its edges. CD is a line in the plane of the plate that passes through the centre of the plate and makes and angle 9 with AB. The moment of inertia of the plate about the axis CD is then equal to

Answers Choices:

I

\(I{\sin ^2}\theta \)

\(I{\cos ^2}\theta \)

\(I{\cos ^2}\left( {\theta /2} \right)\)

Questions 16 of 25

Question:A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin

Answers Choices:

is zero

remains constant

goes on increasing

goes on decreasing

Questions 17 of 25

Question:Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

Answers Choices:

0.42 m from mass of 0.3 kg

0.70 m from mass of 0.7 kg

0.98 m from mass of 0.3 kg

0.98 m from mass of 0.7 kg

Questions 18 of 25

Question:A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega \). The force exerted by the liquid at the other end is

Answers Choices:

M\(\omega \)\(^{\rm{2}}\) L/2

M\(\omega \)\(^{\rm{2}}\)L

M\(\omega \)\(^{\rm{2}}\)L/4

M\(\omega \)\(^{\rm{2}}{{\rm{L}}^{\rm{2}}}/{\rm{2}}\)

Questions 19 of 25

Question:A mass M is moving with a constant velocity parallel to the x-axis. Its angular momentum w.r.t the origin:

Answers Choices:

is zero

remains constant

goes on increasing

goes on decreasing

Questions 20 of 25

Question:A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination\(\theta \). The coefficient of friction between the cylinder and incline is \(\mu \). Then

Answers Choices:

frictional force is always \(\mu \)mg cos\(\theta \)

friction is a dissipative force

by decreasing \(\theta \), frictional force decreases

friction opposes translation and supports rotation.

Questions 21 of 25

Question:A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. Surface BC is . frictionless. \({{\rm{K}}_{\rm{A}}},{\rm{ }}{{\rm{K}}_{\rm{B}}}\) and \({\rm{Kc}}\) are kinetic energies of the ball at A, B and C, respectively. Then

Answers Choices:

\({h_A} > {h_C};{K_B} > {K_C}\)

\({h_A} > {h_C};{K_C} > {K_A}\)

\({h_A} = {h_C};{K_B} = {K_C}\)

\({h_A} < {h_C};{K_B} > {K_C}\)

Questions 22 of 25

Question:The torque \(\vec \tau \) on a body about a given point is found to be equal to \(\vec A \times \vec L\) where \(\vec A\) is a constant vector, and \(\vec L\) is the angular momentum of the body about that point. From this it follows that

Answers Choices:

\(\frac{{d\vec L}}{{dt}}\) is perpendicular to L at all instants of time

the component of \(\vec L\) in the direction of \(\vec A\) does not change with time

the magnitude of \(\vec L\) does not change with time

\(\vec L\)does not change with time

C and D are correct

Questions 23 of 25

Question:The moment of inertia of a thin square plate ABCD, of uniform thickness about an axis passing through the centre O and perpendicular to the plate is

Answers Choices:

\({l_1} + {l_2}\)

\({l_3} + {l_4}\)

\({l_1} + {l_3}\)

\({l_1} + {l_2} + {l_3} + {l_4}\)

Questions 24 of 25

Question:A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v, respectively, strike the bar [as shown in the figure.] and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by\(\omega \), E and \({V_C}\) respectively, we have after collision

Answers Choices:

\({V_C} = 0\)

\(\omega = \frac{{3v}}{{5a}}\)

\(\omega = \frac{v}{{5a}}\)

\(E = \frac{{3m{v^2}}}{5}\)

Questions 25 of 25

Question:A particle of mass m is projected with a velocity V making an angle of \({\rm{45}}^\circ \) with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is,

Answers Choices:

zero

\(m{V^3}/(4\sqrt 2 g)\)

\(m{V^3}/(\sqrt 2 g)\)

\(m\sqrt {2g{h^3}} \)