The speed of a ball of radius $$2 \mathrm{~cm}$$ in a viscous liquid is $$20 \mathrm{~cm} / \mathrm{s}$$. What will be the speed of a ball of radius $$1 \mathrm{~cm}$$ in same liquid?

In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. the intensity of electric field due to the proton at distance 'r' is $$5 \times 10^{11} \mathrm{NC}^{-1}$$, the magnitude of force between the electron and proton is [charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$]

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