Figure shows the arrangement , gas is thermally insulated . Having pressure $\;p_{g}\;$ ( greater than atmospheric pressure $\;p_{a}\;$ ) . Spring of force constant k is initially unstretched . Position of mass m & area S is friction less and in equilibrium position , it rises up a distance $\;x_{0}\;$ , then -

Question

$(a)\;final\;pressure=p_{a}+\large\frac{kx_{0}}{S}+\large\frac{mg}{S}\qquad(b)\;work\;done\;by\;gas=\large\frac{kx_{0}^2}{2}\qquad(c)\;final\;pressure=p_{a}+\large\frac{kx_{0}}{S}\qquad(d)\;work\;done\;by\;gas=\large\frac{kx_{0}^2}{2}+mgx_{0}$