Question

A solid cone of height $H$ , radius $R$ suspended by a string is just submerged in a liquid of density $\rho $ such that tension in string is zero as shown in the figure. The magnitude of the net force applied by the liquid on the curved surface of the cone is equal to (atmospheric pressure is $P_{0}$ )

• A. $\frac{\pi R^{2}}{3}\left(2 P_{0} + \rho g H\right)$
• B. $\frac{\pi R^{3}}{3}\left(2 P_{0} + \rho g H\right)$
• C. $\frac{\pi R^{2}}{3}\left(3 P_{0} + 2 \rho g H\right)$
• D. $\frac{\pi R^{3}}{3}\left(3 P_{0} + 2 \rho g H\right)$

Answer 1

Answer: (C)

There will be only vertically downward force on the curved surface of the cone applied by liquid as the horizontal force will be cancelled.
Let this force is equal to F
Buoyancy force = $\left(P_{0} + \rho g H\right)\pi R^{2}-F$
$\Rightarrow \, \frac{1}{3}\pi R^{2}H\rho g=\left(P_{0} + \rho g H\right)\pi R^{2}-F$
$\Rightarrow \, F=\frac{\pi R^{2}}{3}\left(3 P_{0} + 2 \rho g H\right)$