Question

To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid pressure on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel?

• A. Equal to the radius.
• B. Less than radius
• C. More than radius
• D. Four times of radius

Answer 1

Answer: (A)

Equal to the radius.

If $h$ is the height of liquid in cylinder, $r$ be the radius of the cylinder and $\rho$ be the density of the liquid.

Then we have

Weight of the liquid $=\pi r^{2}h\rho g$........................................(I)

Mean pressure on the wall $=\frac{1}{2}\rho gh$

The total force on the wall = $2\pi rh\times \frac{1}{2}\rho gh=\pi r{h}^2\rho g$....................................(2)

On equating (I) and (2) we have

$\pi r^{2}h\rho g=\pi r{h}^2\rho g$

$r=h$

$\therefore$ The liquid should be filled up-to a height equal to the radius of the cylinder.