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A fixed thermally conducting cylinder ha...

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

A

`((2P_(0)piR^(2))/(piR^(2)P_(0) + Mg))(2L)`

B

`((2P_(0)piR^(2)-Mg)/(piR^(2)P_(0)))(2L)`

C

`((P_(0)piR^(2)+Mg)/(piR^(2)P_(0)))(2L)`

D

`((P_(0)piR^(2))/(piR^(2)P_(0) - Mg))(2L)`

Text Solution

Verified by Experts

The correct Answer is:
D
Mg = `(P_(0) - P) piR^(2) implies P=P_(0) - (Mg)/(piR^(2))`
Since the cylinder is thermally conducting the temperature remains the same.

`P_(0) (2Lxx piR^(2)) = P (yxxpiR^(2)) implies y = ((P_(0) xx piR^(2))/(P_(0)piR^(2) - Mg)) (2L)`
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