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A highly conducting cylindrical vessel placed on elevated small supports contains an ideal gas under a piston of mass m. Area of the base of the cylinder is A. The piston is in equilibrium in the mid of the cylinder. Friction force between the cylinder and the piston can be ignored. Total mass of the cylinder and the gas is M. The atmospheric pressure is $p_{0}$ . Now the piston is slowly pulled upwards, find the maximum value of M such that the cylinder can be lifted off the supports.

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$\frac{2 p_{0} A - m g}{2 g}$

It is impossible in this way

$\frac{p_{0} A - m g}{2 g}$

$\frac{p_{0} A - m g}{g}$

answer is B.

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Detailed Solution

Equilibrium condition for
cylinder ares gas are
$M g + \frac{d}{2} (P_{0} + \frac{M g}{A}) A = P_{0} A$
$2 M g + P_{0} A + M g$
$M = \frac{P_{0} g}{2 g}$
$2 M g + P_{0} A + M g = 2 P_{0} A$
$m = \frac{P_{0} A - M g}{2 g} g$

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