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.
1.17×105Nm-2 -
D.
1.03 x 105Nm-2 -
E.
1.36 x104 Nm-2
Correct Answer: Option 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})