An e.m.f. $E=E_0 \cos \omega t$ is applied to the $L-R$ circuit. The inductive reactance is equal to the resistance ' $R$ ' of the circuit. The power consumed in the circuit is

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