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A fixed thermally conducting cylinder has a radius \( \mathrm{R} \) and height \( \mathrm{L}_{0} \). 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 \( \mathrm{L} \) from the top surface, as shown in the figure. The atmospheric pressure is \( \mathrm{P}_{0} \).
While the piston is at a distance \( 2 \mathrm{~L} \) from the top, the hole at the top is sealed. The piston is then release to a position where it can stay in equilibrium. In the condition, the distance of the piston from the top is
(1) \( \left(\frac{2 P_{0} \pi R^{2}}{\pi R^{2} P_{0}+M g}\right)(2 L) \)
(2) \( \left(\frac{P_{0} \pi R^{2}-M g}{\pi R^{2} P_{0}}\right)(2 L) \downarrow \)
(3) \( \left(\frac{P_{0} \pi R^{2}+M g}{\pi R^{2} P_{0}}\right)(2 L) \)
(4) \( \left(\frac{P_{0} \pi R^{2}}{\pi R^{2} P_{0}-M g}\right)(2 L) \)
Piston


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