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

Two parallel plate air c apacitors of same capacity ' C ' are connected in parallel to a battery of e.m.f. ' $E$ '. Then one of the capacitors is completely filled with dielectric mnaterial of constant ' K '. The change in the effective capacity of the parallel combination is

An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' $V$ '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' P '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is

The escape velocity of a satellite from the surface of earth does NOT depend on