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

When the piston is pulled out slowly, the pressure drop produced inside the cylinder is almost instantaneously neutralized 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.