A small circular membrane is 10cm below the surface of a pool of mercury when the barometric height is 76 cm of mercury. If the density of mercury is 13600\(kgm^{-3}\), what is the pressure on the membrane in \(Nm^{-2}\)? \((g =10ms^{-2})\)
A. 1.17 x 107 Nm-2 B. 6.80 x 105Nm-2 C. 1.17x105Nm-2 D. 1.03 x 105Nm-2 E. 1.36 x104 Nm-2
Correct Answer: C
Explanation
Pressure at a depth for fluid with constant density such as mercury is given as \(p = p_{0} + \rho hg\) where \(p_{0}\) = atmospheric pressure. \(p_{0} = \rho hg =13600 \times \frac{76}{100} \times 10\) = \(103,360 Nm^{-2}\) \(p = 103,360 + (13600 \times \frac{10}{100} \times 10)\) \(p = 103,360 + 13,600\) \(p = 116,960 Nm^{-2} \approxeq 1.17 \times 10^{5} Nm^{-2}\)
