The density of air in the Earth’s atmosphere falls by almost a straight-line relationship as height increases, dropping from $1.22\,\text{kg m}^{-3}$ at sea level to $0.74\,\text{kg m}^{-3}$ at an altitude of $5000\,\text{m}$. On a certain day, the atmospheric pressure at the Earth’s surface is $100\,000\,\text{Pa}$. Over the region from the Earth’s surface up to an altitude of $5000\,\text{m}$, $g$ may be taken as constant at $9.7\,\text{m s}^{-2}$. What is the atmospheric pressure at an altitude of $5000\,\text{m}$?
- A$36\,000\,\text{Pa}$
- B$48\,000\,\text{Pa}$
- C$52\,000\,\text{Pa}$
- D$59\,000\,\text{Pa}$