Mercury fills a U-tube that is sealed at one end. Air, at a pressure of $5.0 \times 10^4\,\text{Pa}$, is trapped in the closed end. The opposite end is exposed to the atmosphere and has a piston of mass $5.0\,\text{kg}$ and cross-sectional area $5.0 \times 10^{-4}\,\text{m}^2$. The density of mercury is $13\,600\,\text{kg m}^{-3}$ and atmospheric pressure is $1.01 \times 10^5\,\text{Pa}$. Determine the height $h$ of the mercury column.
- A$37\,\text{cm}$
- B$44\,\text{cm}$
- C$74\,\text{cm}$
- D$110\,\text{cm}$