In an $L-R$ circuit, the inductive reactance is equal to $\sqrt{3}$ times the resistance ' $R$ ' of the circuit. An e.1n.f. $\mathrm{E}=\mathrm{E}_0 \sin (\omega \mathrm{t})$ is applied to the circuit. The power consumed in the circuit is

A charged particle of mass ' $m$ ' and charge ' $q$ ' is at rest. It is acce:lerated in a uniform electric field of intensity ' $E$ ' : for time ' $t$ '. The kinetic energy of the particles after time $t$ is

To determine the internal resistance of a cell with potentiometer, when the cell is shunted by a resistance of $5 \Omega$ the balancing length is 250 cm . When the cell is shunted by $20 \Omega$, the balancing length of potentiometer wire is 400 cm . The internal resistance , of the cell is

A body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity V . If the same body is a ring which rolls down the same inclined plane then linear velocity at the bottom of plane is