Rotational Work and Energy

Q. A flywheel of moment of inertia $0.32kg-m^2$ is rotated steadily at 120 rad/sec by an electric motor. The kinetic energy of the flywheel is

1. 4608 J
2. 1152 J
3. 2304 J
4. 6912 J

Q. If the angular momentum of a rotating body is increased by $200\%,$ then its kinetic energy of rotation will be increased by

1. $400\%$
2. $200\%$
3. $100\%$
4. $800\%$

Q. A tangential force of 10 N is applied on the periphery of a ring due to which it starts rotating about an axis through its centre and perpendicular to its plane. What is the work done by this force in rotating the ring by ${45}^o$? {R = 2m}.

1. $4\pi J$
2. $5\pi J$
3. $10\pi J$
4. $15\pi J$

Q. Two bodies rotating with the same angular momentum have M.I. $I_{1}and{I}_2$ respectively such as $I_1>I_2$ respectively, then

1. $E_2>E_1$
2. $E_1>E_2$
3. $E_2=E_1$
4. $E_1=2E_2$

Q. A ring, a solid sphere and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest

1. Disc
2. Ring
3. Solid sphere
4. All will make same number of rotations

Q.

In the shown figure, a particle of mass 'm' slides down the frictionless surface from height 'h' and collides with the uniform vertical rod of length L and mass M. After the collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about a fixed axis through O. Find the cosine of the maximum angular deflection of the rod from its initial position.

1. $1-\frac{m^2{v}_0^2}{2(m+\frac{M}{3})(m+\frac{M}{2})gL}$

2. $1-\frac{M^2{v}_0^2}{(m+\frac{M}{3})(m+\frac{M}{2})gL}$

3. $1-\frac{M^2{v}_0^2}{2(m+\frac{M}{3})(m+\frac{M}{2})gL}$

4. $1-\frac{m^2{v}_0^2}{(m+\frac{M}{3})(m+\frac{M}{2})gL}$

Q. If each point mass of a rigid ring covers a distance of $\frac{\pi }{2}m,$ by how much angle (in radians) the ring has been rotated? (R = 2m)

1. $\frac{\pi }{2}radians$
2. $\frac{3\pi }{4}radians$
3. $\pi$ radians
4. $\frac{\pi }{4}radians$

Q. When a solid sphere is rolling along level surface the percentage of its total kinetic energy that is transnational is

1. $29$
2. $71$
3. $60$
4. $40$