Water flows into a large tank with flat bottom at the rate f 10^-4m³s^-1. Water is also leaking out of a hole of area 1 cm² at its bottom. If the height of the water in the tank remains steady. then this height (in cm) is _______ $\times$ 10^-1

Water inflow rate = ${10}^{-4}{m}^3{s}^{-1}$

Area of the hole = $1c{m}^2=1\times {10}^{-4}{m}^2={10}^{-4}{m}^2$

Since the water level in the tank doesn't change over time, (Water inflow rate) = (Outflow rate of water)

${10}^{-4}{m}^3{s}^{-1}={10}^{-4}\times \sqrt{2gh}$

$\sqrt{2gh}=1$

$2\times 9.8\times h=1^2$

$h=\frac{1}{9.8\times 2}$

$h=\frac{1}{19.6}$

$h=\frac{100}{19.6}$

$h=5.1cm$

$h=51\times {10}^{-1}$

Hence the correct answer is 51.