Water is poured in a vessel at a constant rate $β m^{3} / s .$ . There is a small hole of area $α$ at the bottom of the vessel. The maximum level of water in the vessel is proportional to :

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$β / α$

$β^{2} / α$

$β^{2} / α^{2}$

$α^{2} / β^{2}$

answer is C.

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Detailed Solution

When water attains maximum level, rate of inflow will be equal to rate of outflow.
$β = αv = α \sqrt{2 gh} \Rightarrow \frac{β^{2}}{α^{2}} = 2 gh \Rightarrow h \infty \frac{β^{2}}{α^{2}}$

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