Question

To what height should a rectangular cylinder having square base of length $10cm$ be filled so that the total force on the bottom is equal to that on the sides-

• A. $5cm$
• B. $10cm$
• C. $20cm$
• D. $6.67cm$

Answer 1

Answer: (A)

$5cm$

Given,

$l=10cm$

$g=10m/s^2$

Let's consider $h$ is the height of the cylinder.

The pressure at bottom,

$P=\rho gh$. . . . . .(1)

The pressure at sides

$P^{\prime }=\frac{\rho gh}{2}$. . . . . .(2)

Base is square, so area $a=l^2={10}^2=100c{m}^2$

Area of one side,

$A=h\times l=h\times 10=10h$

So, $Pa=P^{\prime }A$

$\rho gh\times 100=4\times \frac{\rho gh}{2}\times 10h$

$200=40h$

$h=\frac{200}{40}$

$h=5cm$

The correct option is A.