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 `l_(1)`, and that below the piston is `l_(2)`, such that `l_(1)gtl_(2)`. Each part of the cylinder contains n moles of an ideal gas at equal temeprature T. If the pistion is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravitey)

Options

A. `(RT)/(ng)[(l_(1)-3l_(2))/(l_(1)l_(2))]`
B. `(nRT)/(g)[(l_(1)-l_(2))/(l_(1)l_(2))]`
C. `(nRT)/(g)[(1)/(l_(2))+(1)/(l_(1))]`
D. `(RT)/(gl)[(2l_(1)+l_(2))/(l_(1)l_(2))]`

Answer

B