Question

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

• A. $2\pi R^3\rho g$
• 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 D None of these

The volume of cylinder radius is given by

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

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

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

Now the force required to stop the rotation

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