A particle performing S.H.M. when displacement is '$$x$$', the potential energy and restoring force acting on it are denoted by '$$E$$' and '$$F$$' respectively. The relation between $$x, E$$ and $$F$$ is

A molecule consists of two atoms each of mass '$$m$$' and separated by a distance '$$\mathrm{d}$$'. At room temperature, if the average rotational kinetic energy is '$$E$$' then the angular frequency is

The magnifying power of a refracting type of astronomical telescope is '$$\mathrm{m}$$'. If focal length of eyepiece is doubled then the magnifying power will become

A wooden black of mass '$$\mathrm{m}$$' moves with velocity '$$\mathrm{V}$$' and collides with another block of mass '$$4 \mathrm{~m}$$', which is at rest. After collision the block of mass '$$\mathrm{m}$$' comes to rest. The coefficient of restitution will be