Question

A cylinder has a radius r. To what height h should it be filled with water so that the thrust on its walls is equal to that on its bottom:

• A. h = 2r
• B. h = r
• C. h = (r/2)
• D. h = (r/4)

Answer 1

The correct option is B h = r

Let the height upto which the water is filled be $h$.

Area of the bottom $A_b=\pi r^2$

Pressure exerted at the bottom $P_b=\rho gh$

$\therefore$ Thrust at the bottom $T_b=\rho gh\left(\pi r^2\right)$

For the walls : Force exerted at the walls $F=P_{CM}A$

$\therefore$ $F=\rho g\frac{h}{2}\times 2\pi rh$

According to the question, $F=T_b$

$\therefore$ $\rho g\frac{h}{2}\times 2\pi rh=\rho gh\left(\pi r^2\right)$ $⟹h=r$