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As shown, a piston chamber of cross section area $A$ is filled with ideal gas. A sealed piston of mass $m$ is right at the middle height of the cylinder at equilibrium. The friction force between the chamber wall and the piston can be ignored. The mass of the rest of the chamber is $M$ . The atmosphere pressure is $P_{0} .$ Now slowly pull the piston upwards. Gas expands isothermally. Find the minimum value of $\frac{m}{M}$ such that the chamber can be lifted off the ground. Given that $P_{0} = \frac{4 m g}{3 A} .$

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answer is 6.

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Detailed Solution

Initially
$P_{1} = P_{0} + \frac{m g}{A} = \frac{7}{3} \frac{m g}{A}$
Finally
$P_{2} = P_{0} - \frac{M g}{A} = (\frac{4}{3} m - M) \frac{g}{A}$
$P_{1} \frac{V}{2} = P_{2} V$

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