A solid cylinder of mass ' $M$ ' and radius ' $R$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the foot of the plane, its rotational kinetic energy is ( $\mathrm{g}=$ acceleration due to gravity)

The maximum velocity and maximum acceleration of a particle performing a linear S.H.M. is ' $\alpha$ ' and ' $\beta$ ' respectively. Then the path length of the particle is

When a galvanometer is shunted by a resistance ' $s$ ', its current capacity increases ' $n$ ' times. If the same galvanometer is shunted by another resistance ' $s_1$ ', its capacity will increase to ' $n_1$ ' times original current. The value of ' $n_1$ ' is

A pergect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will