Question

To what height h should a cylindrical vessel of diameter d be filled with a liquid so that the total force on the vertical surface of the vessel be equal to the force on the bottom-

• A. $h=d$
• B. $h=2d$
• C. $h=3d$
• D. $h=d/2$

Answer 1

The correct option is D $h=d/2$

If we fill the cylinder upto a height h, the force exerted on at the bottom of the cylinder would be equal to F = PA

$F=\rho gh\times \pi d^2/4$

Similarly, the average force exerted along the sides of the cylinder will be because of half the height filled for the cylinder.

Therefore, $F=\rho gh/2\times \pi dh$

Equating the 2 forces, and solving for h, gives h = d/2