Water flows into a large tank with flat bottom at the rate of ${10^{ - 4}}\,{m^3}{s^{ - 1}}$. Water is also leaking out of a hole of area $1\, cm^2$ at its bottom. If the height of the water in the tank remains steady, then this height is........ $cm$
JEE MAIN 2019, Medium
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$\frac{{dv}}{{dt}} = \phi - a\sqrt {2gh} = 0$ $(for\,maximum\,height)$
$h = \frac{{{\phi ^2}}}{{2g{a^2}}} = \frac{{{{10}^{ - 8}}}}{{2 \times 9.8 \times {{10}^{ - 8}}}} = 5.1\,cm$
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