Rotational Motion

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of \(60^\circ\) with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take g = 10 m/s\(^2\))

A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm\(^2\). The length of the 400 g rod is nearly :

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is \(v\) in the direction shown, which one of the following options is correct (\(P\) and \(Q\) are any highest and lowest points on the wheel, respectively)?

The ratio of radius of gyration of a solid sphere of mass \(M\) and radius \(R\) about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is :

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s\(^2\) is :

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. (g = 10 m/s\(^2\))

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times 'MR\(^2\)'. Then the value of 'K' is :

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.

The centre of mass of the system from the 5 kg particle is nearly at a distance of :

Find the torque about the origin when a force of \(3\hat{j}\) N acts on a particle whose position vector is \(2\hat{k}\) m.

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?

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 \(2\pi\) revolutions is :

The moment of the force, \(\vec F=4\hat i+5\hat j-6\hat k\) at (2, 0, \(-\)3), about the point (2, \(-\)2, \(-\)2), is given by

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 \(\omega\) about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

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

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 ?

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities \(\omega_1\) and \(\omega_2\). They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is :

Which of the following statements are correct ?

(a) Centre of mass of a body always coincides with the centre of gravity of the body.

(b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.

(c) A couple on a body produce both translational and rotational motion in a body.

(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ?

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of \(2.0\ rad\ s^{-2}\). Its net acceleration in \(ms^{-2}\) at the end of 2.0 s is approximately :

A disk 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 ?

A solid sphere of mass \(m\) and radius \(R\) is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (\(E_{sphere}/E_{cylinder}\)) will be

A light rod of length \(l\) has two masses \(m_1\) and \(m_2\) attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

Two rotating bodies \(A\) and \(B\) of masses \(m\) and \(2m\) 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