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

An electron of mass ' $m$ ' and charge ' $q$ ' is accelerated from rest in a uniform electric field of intensity ' $E$ '. The velocity acquired by it as it travels a distance ' $l$ ' is ' $v$ '. The ratio $\frac{\mathrm{q}}{\mathrm{m}}$ in terms of $E, l$ and $v$ is