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 $\ell_1$ , and that below the piston is $\ell_2$ , such that $\ell_1$ > $\ell_2$ . 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)

$\frac{nRT}{g} \bigg[\frac{\ell_1 - \ell_2}{\ell_1\ell_2} \bigg]$

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 $\ell_1$ , and that below the piston is $\ell_2$ , such that $\ell_1$ > $\ell_2$ . 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)}

$\frac{nRT}{g} \bigg[\frac{\ell_1 - \ell_2}{\ell_1\ell_2} \bigg]$

$\frac{nRT}{g} \bigg[\frac{1}{\ell_2} + \frac{1}{\ell_1}\bigg]$

$\frac{nRT}{g} \bigg[\frac{\ell_1 - \ell_2}{\ell_1\ell_2} \bigg]$

$\frac{RT}{g} \bigg[\frac{2\ell_1 + \ell_2}{\ell_1 \ell_2} \bigg]$

$\frac{RT}{g} \bigg[\frac{\ell_1 - 3\ell_2}{\ell_1\ell_2} \bigg]$

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