Question

A light semi cylindrical gate of radius $R$ is pivoted at its mid point $O$, of the diameter holding liquid of density $\rho$ as shown in the figure. The force $F$ required to prevent the rotation of the gate is equal to

• A. $\pi R^2\rho g$h
• B. $2\rho g{R}^{3}l$
• C. $\frac{2R^{2}l\rho g}{3}$
• D. None of these

Answer 1

The correct option is A $\pi R^2\rho g$h

The volume of cylinder of radius $R$ is given by

$v=\pi R^{2}h$

mass $=m=\pi R^{2}h\rho$

weight $=w=\pi R^{2}h\rho g$

Now force required to stop rotation of gate in

$f=\pi R^{2}h\varphi g$