Water flows into a large tank with flat bottom at the rate of ${10}^{-4}{\text{m}}^3{\text{s}}^{-1}$. Water is also leaking out of a hole of area $1{\text{cm}}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is:

The correct option is A $5.1\text{cm}$
Given:
Water in flow rate $Q_{in}={10}^{-4}{\text{m}}^3{\text{s}}^{-1}$.
Leaking hole area $A=1{\text{cm}}^2$


Since height of water column is constant therefore,
water inflow rate $\left(Q_{\text{in}}\right)$
= water outflow rate

$Q_{in}=Q_{out}$

${10}^{-4}=Au=1\times {10}^{-4}\times \sqrt{2gh}(\because u=\sqrt{2gh})$

$\therefore {10}^{-4}={10}^{-4}\times \sqrt{2\times 9.8\times h}$

$\therefore h=\frac{1}{2\times 9.8}\text{m}=0.051\text{m}$

$h=5.1\text{cm}$

Hence, option $\left(A\right)$ is correct.