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

A body is rolling down an inclined plane. If kinetic energy of rotation is $40\%$ of  translational kinetic energy, then the body is a

The speed of rolling of a ring of mass $M$ changes from $V$to $3\ V$. What is the change in its kinetic energy

A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is 

A solid sphere rolls without slipping and presses a spring of spring constant $k$ as shown in figure. Then, the maximum compression in the spring will be

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches upto a maximum height of $3v^2/4g$ with respect to the initial position. The object is