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A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is A 1 , and that below the piston is A 2 , such that A 1 > A 2 . Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)

1. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 2 1 – g nRT A A A A
2. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + 2 1 2 1 2 g RT A A A A
3. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + 1 2 1 1 g nRT A A
4. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 2 1 3 – ng RT A A A A

Correct answer: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 2 1 – g nRT A A A A

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