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?

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 

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 hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is________.

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