Question

A cylinder has a radius $10\text{cm}$. What height should it be filled with water so that the thrust at its walls is equal to that on its bottom?

• A. $10\text{cm}$
• B. $0.2\text{cm}$
• C. $2.5\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is A $10\text{cm}$

Let
$\rho =$ density of water
$h=$ height of water in cylinder
$f=$ thrust on the bottom
then, $f=\text{Pressure}\times \text{Area}=\rho gh\times \pi r^2$
If we talk about the walls then, thrust on the walls $f^{\prime }$ is
$f^{\prime }=\text{Average pressure}\times \text{Area}$
$f^{\prime }=\frac{\rho gh}{2}\times \left(2\pi rh\right)$
Given $f=f^{\prime }\Rightarrow h\rho g\times \pi r^2=\rho g{h}^2\pi r$
$\Rightarrow h=r$
$\Rightarrow h=10\text{cm}$