Question

The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel is equal to:

• A. half of the radius of the vessel.
• B. radius of the vessel.
• C. one-fifth of the radius of the vessel.
• D. three-fourth of the radius of the vessel.

Answer 1

Answer: (B)

radius of the vessel.

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 $=\pi r^{2}h\rho g.......\left(I\right)$
Mean pressure on the wall $=\frac{1}{2}\rho gh$
force on the wall $=\frac{1}{2}\rho gh\times 2\pi rh=\pi r\rho g{h}^2.......\left(II\right)$
On equating $\left(I\right)$ and $\left(II\right)$ we have
$\pi r^{2}h\rho g=\pi r\rho g{h}^2$
$\Rightarrow r=h$
i.e. the liquid should be filled up-to a height equal to the radius of the cylinder.