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 l₁ and that below the piston is l₂, such that l₁ > l₂. 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)

The correct option is B
nRTg[(l₁ - l₂)/l₁l₂]
P₂A = P₁A + mg
where P₁ and P₂ are the pressures in the upper and lower parts of the cylinder respectively, A is the cross-sectional area of the cylinder, and g is the acceleration due to gravity.
According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
In the upper part of the cylinder, the pressure is P₁ = nRT/(Al₁)
In the lower part of the cylinder, the pressure is P₂ = nRT/(Al₂)
Substituting these values into the equation P₂A = P₁A + mg, we get:
(nRT/l₂) = (nRT/l₁) + mg
m = (nRT/g)[(1/l₂) - (1/l₁)] = nRTg[(l₁ - l₂)/l₁l₂]