Question

A cylindrical tank has a hole of area $1{\text{cm}}^2$ at its bottom. If water is allowed to flow into the tank from a tube above it at the rate of $70{\text{cm}}^3/\text{sec}$, then the maximum height up to which water can rise in the tank is -
[Take $g=980{\text{cm/s}}^2$]

• A. $2.5\text{cm}$
• B. $5\text{cm}$
• C. $10\text{cm}$
• D. $0.25\text{cm}$

Answer 1

The correct option is A $2.5\text{cm}$

The height of water in the tank becomes maximum when the volume of water flowing into the tank per second becomes equal to the volume of water flowing out per second.

We know, volume of water flowing out per second,
$Q_{out}=Av=A\sqrt{2gh}$ .........(1)
where $h$ is the height of water at any instant.
Given, volume of water flowing in per second,
$Q_{in}=70{\text{cm}}^3/s$ .........(2)
From (1) and (2),
$A\sqrt{2gh}=70$
$\Rightarrow 1\times \sqrt{2\times 980\times h}=70$
$[$ given, $A=1{\text{cm}}^2]$
$\Rightarrow h=\frac{4900}{1960}=2.5\text{cm}$