As shown , a piston chamber pf cross section area `A` is filled with ideal gas. `A` sealed piston of mass m is right at the middle height of the cylinder at equilibrium. The friction force between the chamber wall and the piston can be ignored . The mass of the rest of the chamber is `M`.The atmosphere pressure is `P_(0)`. Now slowly pull the piston upwards , find the maximum value of `M` such that the chamber can be lifted off the ground. The temperature remains unchanged.

Options

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

Answer

B

Explanation

`P_(f)V_(f) = P_(f)V_(f)`
where `V_(L) = (V_(f))/(2)`