Question

A uniform solid hemisphere of radius R is immersed into a liquid of density \(\rho\) as shown. The base of the hemisphere is at distance R from the surface of the liquid. Ignore atmospheric pressure. The force by the liquid on the curved surface of the hemisphere is

• A. $\frac{4\pi }{3}\rho g{R}^3$
• B. $\pi \rho g{R}^3$
• C. $\frac{5\pi }{3}\rho g{R}^3$
• D. $\frac{2\pi }{3}\rho g{R}^3$

Answer 1

The correct option is C $\frac{5\pi }{3}\rho g{R}^3$

$F_c-\rho gR.\pi R^2=\frac{2\pi }{3}{R}^3\rho g$
$\Rightarrow F_c=\frac{5}{3}\pi \rho g{R}^3$