An ideal gas ($\gamma = 1.5$) is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded

A spring force constant $180$ N/m is loaded with a mass $0.2$ kg. The amplitude of oscillations is $4$ cm. When mass comes to equilibrium position, its velocity is

A particle executing linear S.H.M. has velocities $V_1$ and $V_2$ at distance $x_1$ and $x_2$ respectively, from the mean position, its angular velocity is

In a resonance tube open at one end, the end correction is $1.1$ cm. If the shortest length of resonating air column with a tuning fork is $18$ cm, the next resonating length will be