For a gas, $\dfrac{R}{C_v} = 0.4$ where R is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are

An oscillating pendulum suspended from the roof of a lift which is at rest has time period $T_1$. When lift moves up with acceleration 'a' its time period is $T_2$. When lift moves down with acceleration 'a' its time period is $T_3$. The relation between $T_1$, $T_2$ and $T_3$ is

A mass $0.4$ kg performs S.H.M. with a frequency $\dfrac{16}{\pi}$ Hz. At a certain displacement it has kinetic energy $2$ J and potential energy $1.2$ J. The amplitude of oscillation is

A mass attached to a spring performs S.H.M. whose displacement is $x = 3 \times 10^{-3} \cos 2\pi t$ m. The time taken to obtain maximum speed for the first time is (in s)