Figure shows initial state of an ideal gas trapped in a container with conducting walls and a piston (mass `m`) which can move without any friction. The container is placed on point supports and its wall are conducting. Assuming that atmospheric pressure is `P_(0)` and the mass of the ideal gas is negligible as compared to the mass of the piston and the mass of container. Take the cross section area of piston to be A. The piston is slowly lifted by an external agent and held in its position. Let `M` be the maximum mass of container so that it may "lift off" while pulling the piston upwards and `P_(i)` be the pressure of ideal gas in initial state. Pick the correct choice:

Options

A. `P_(i)=P_(0)+(mg)/A`
B. `P_(i)=(P_(0))/2+(mg)/(2A)`
C. `M=m/2`
D. `M=(P_(0)A)/(2g)-m/2`

Answer

A, D

Explanation

`Mg+PA=P_(0)A`
`M=(P_(0)A)/g-(PA)/g`
`P=(P_(i))/2=(P_(0)+(mg)/A)/2`
`impliesM=(P_(0)A)/(2g)-m/2`