The fixed non-conducting cylinder shown in figure has a noconducting heavy piston of mass `M` that can slide without friction. The area of piston is `S` and the cylinder is filled with an ideal gas `(lambda=1.5)` with an initial volume `V` and an initial pressure `P`. Assume that the outside pressure on the piston is zero (vaccum). (Neglect acceleration due to gravity).

After the piston has moved by distance `S`. Its velocity is:

Options

A. `((4PV)/(M)[1-((V)/(V+LS))^(1//2)])^(1//2)`
B. `((4PV)/(M)[1-((V)/(V+LS))])^(1//2)`
C. `((4PV)/(M)[1-((V+LS)/(V))^(1//2)])^(1//2)`
D. None of these

Explanation

Workdone by gas in the adiabatic process
`2PV[1-((V)/(V+LS))^(1//2)]`
`therefore(1)/(2)Mv^(2)=DeltaW`
`thereforev=((4PC)/(M)[1-((V)/(V+LS))^(1//2)])^(1//2)`