An insulated container contains a monoatomic gas of molar mass 'm'. The container is moving with velocity 'V'. If it is stopped suddenly, the change in temperature of the gas is (R-gas constant)

Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $0.2$. When $T_2$ is lowered by $45$ K, its efficiency becomes $0.5$. Temperatures $T_1$ and $T_2$ are respectively

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