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

Two charged metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that of the smaller sphere, the electric field near the larger sphere is