Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 63 K then the rise in temperature of the gas in A is

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ$ C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)

The displacement of a particle performing linear S.H.M. is given by $y = A\cos[\pi(t + \phi)]$. If at $t = 0$, the displacement is $y = 2$ cm and velocity is $2\pi$ cm/s, the value of amplitude A in cm is

A light spring is suspended with mass '$m_1$' at its lower end and its upper end is fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass '$m_2$' is added to '$m_1$' and the system is made to oscillate the period is found to be $\dfrac{3}{2}$ T. The ratio $\left(\dfrac{m_1}{m_2}\right)$ is