A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\dfrac{1}{8}\right)^{th}$ of its initial volume. The ratio of final pressure to initial pressure is

The average force applied on the walls of a closed container depends on temperature (T) as (T is the temperature of an ideal gas)

A particle executes linear S.H.M. with amplitude $4$ cm. The magnitude of velocity and acceleration is equal when it is at $3$ cm from mean position. Time period is

A particle starts from mean position and performs S.H.M. with period $6$ second. At what time its kinetic energy is $50\%$ of total energy? ($\cos 45^\circ = 1/\sqrt{2}$)