An ideal gas with pressure P, volume V and temperature T is expanded isothermally to volume 2V and a final pressure $P_i$. The same gas is expanded adiabatically to a volume 2V then the final pressure is $P_a$. In terms of $\gamma$, the ratio of the two specific heats for the gas, the ratio $P_i / P_a$ is

At a pressure P and temperature T, 7 gram of oxygen occupies a volume V. The equation of state will be (Molecular weight of Oxygen $= 32$)

When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$'. Out of the following relations, the true one is

Three masses 100g, 300g and 500g are suspended at the end of a spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is also removed, it will oscillate with a period of