Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a mono-atomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\gamma_1 / \gamma_2$ is

A block is fastened to a horizontal spring. The block is pulled to a distance $x = 10$ cm from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The kinetic energy of the block at $x = 5$ cm is $0.25$ J. The spring constant of the spring is nearly (in $\text{Nm}^{-1}$)

The amplitude of a particle executing SHM is $3$ cm. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is (in cm)

The velocity of a particle executing SHM varies with displacement ($x$) as $4v^2 = 50 - x^2$.
The time period of oscillations is $x/7$ s.
The value of $x$ is (Take $\pi = 22/7$)