Nodal analysis is generally used to determine______

Options

A. Voltage
B. Current
C. Resistance
D. Power

Explanation

`Let l_(1) and l_(2)` be the upper part and the lower part of the cylinder respectively. Clearly, `l_(1)=50cm` and `l_(2)=40cm`. Let the pressures in the upper and lower parts be `p_(1)` and `p_(2)` respectively. Let the area of creoss section of the cylinder be `A`. The temperature in both parts is `T=300K`.
Consider the equilbrium of the piston . the forces acting on the piston are
(a) its weight mg
(b) `p_(1)` A downward, by the upper part of the gas
and (c) `p_(2)` A upward, by the lower part of gas .
Thus , `p_(2) A =p_(1)A +mg` ....(i)
Using `pV=nRt` for the upper and the lower parts
`p_(1)l_(1)A=nRT` ...(ii)
and `p_(2)l_(2)A=nRT` (iii)
Putting `p_(1) A and p_(2)A` from (ii)and(iii) into(i),
`(nRT)/(l_(2))=(nRT)/(l_(1))+mg`
Thus, `m=(nRT)/(g)[(1)/(l_(2))-(1)/(l_(1))]`
`=((0.1 mol)(8.3JK^(-1) mol^(-1))(300K))/(9.8ms^(-2)[(1)/(0.4m)-(1)/(0.5m)]`
`=12.7kg.`