Question

The level of water in a tank is $5\text{m}$ high. A hole of area $1{\text{cm}}^2$ is made at the bottom of the tank. The rate of leakage of water from the hole is : [Take $g=10{\text{m/s}}^2$]

• A. ${10}^{-3}\text{m}{}^3\text{/s}$
• B. ${10}^{-4}\text{m}{}^3\text{/s}$
• C. ${10}^{-2}\text{m}{}^3\text{/s}$
• D. ${10}^{-1}\text{m}{}^3\text{/s}$

Answer 1

The correct option is A ${10}^{-3}\text{m}{}^3\text{/s}$

Given,
Height of the surface of water in the tank, $h=5\text{m}$
Area of hole, $A=1{\text{cm}}^2=1\times {10}^{-4}{\text{m}}^2$
We know that rate of leakage of water, $Q=Av=A\sqrt{2gh}$
$={10}^{-4}\times \sqrt{2\times 10\times 5}$
$={10}^{-3}\text{m}{}^3\text{/s}$