Q 11-09-059JEE MainJEE Main 2024 (4 Apr, Shift 2)Medium
Mercury is filled in a tube of radius $2\ \text{cm}$ up to a height of $30\ \text{cm}$. The force exerted by the mercury on the bottom of the tube is ______ N. (Given: atmospheric pressure $= 10^5\ \text{N m}^{-2}$, density of mercury $= 1.36\times10^4\ \text{kg m}^{-3}$, $g = 10\ \text{m s}^{-2}$, $\pi = \dfrac{22}{7}$)
Numerical value type. Enter your answer.
Answer: 177
Pressure at the bottom (the open tube has atmosphere on top):
$$P = P_0 + \rho gh = 10^5 + 1.36\times10^4\times10\times0.3 = 1.408\times10^5\ \text{Pa}$$
$$F = PA = 1.408\times10^5\times\frac{22}{7}\times(0.02)^2 \approx 177\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics