A mass $m$ rests on a platform, which is held up by gas inside a cylinder of cross-sectional area $A$, as illustrated. The platform has negligible mass and is free to move vertically. The gas is heated and expands, causing the mass to rise by a height $h$. Atmospheric pressure is $p$. What is the ratio $\frac{\text{gain in gravitational potential energy of the mass}}{\text{work done by the gas}}$?
- A$\frac{mg}{pA}$
- B$\frac{mg}{mg + pA}$
- C$\frac{pA}{mg}$
- D$\frac{mg - pA}{mg}$