The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth to the escape velocity at a planet is

A black sphere has radius $R$ whose rate of radiation is E at temperature T . If radius is made half and temperature 4 T , the rate of radiation will be

If the ionisation energy for the hydrogen atom is 13.6 eV , then the energy required to excite it from the ground state to the next higher state is nearly

A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $\mathrm{P}_2$. The speed of water flowing out of the pipe is ($\rho=$ density of water)