A fixed thermally conducting cylinder has a radius R and height `L_0`. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is `P_0`.

While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

Options

A. `((2P_0 piR^2)/(pi R^2 P_0 + Mg))(2L)`
B. `((P_0 pi R^2-Mg)/(pi R^2 P_0))(2L)`
C. `((P_0 pi R^2+Mg)/(pi R^2 P_0))(2L)`
D. `((P_0 pi R^2)/(pi R^2 P_-0 - Mg))(2L)`

Answer

D

Explanation

Let p be the pressure in equilibrium, then `pA = P_0 A - Mg`
Applying `P_1 V_1 = P_2 V_2`
`L'=(2P_0L)/P =((p_0)/(p_0-(Mg)/(piR^2)))(2L) = ((P_0 pi R^2)/(pi R^2 P_0 - Mg)) (2L)`
Therefore, option (D) is correct.