A fixed thermally conducting cylinder has a radius R and height `L_0`. The cylinder is open at ita 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`.

The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

Options

A. `P_0`
B. `(P_0)/2`
C. `(P_0)/2+(Mg)/(piR^2)`
D. `(P_0)/2-(Mg)/(piR^2)`

Answer

A

Explanation

(a) When the piston is pulled out slowly, the
pressure drop produced inside the cylinder is almost
instantaneously neutralised by the air entering from
outside into the cylinder (through the small hole at the
top).
Therefore , the pressure inside the cylinder is `P_0`
throughout the slow pulling process.