An ideal rigid diatomic gas $\left(\gamma = \dfrac{7}{5}\right)$ undergoes an adiabatic change . If the relation between temperature and volume is $TV^x = $ constant then the value of x is

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters $2P$, $\dfrac{V}{4}$, $2T$. The ratio of number of molecules of jar B to those of jar A is

A simple pendulum of length $l_1$ has periodic time $2.4$ s. Another simple pendulum of length $l_2 < l_1$, has periodic time $1.8$ s. The periodic time of simple pendulum of length $(l_1 - l_2)$ is nearly

Two springs of force constants '$2k$' and '$k$' are connected to a mass '$m$' as shown. Mass is displaced slightly to one side and released. The frequency of oscillation of the two springs-mass system is