Water flows into a large tank with flat bottom at a rate of 10-4m3 / s. Water is also leaking out of a hole of area 1cm2 at its bottom. The height of the water in the tank is ________cm(if the height is steady)

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Water flows into a large tank with flat bottom at a rate of 10^-4m³ / s. Water is also leaking out of a hole of area 1cm² at its bottom. The height of the water in the tank is ________cm(if the height is steady)

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answer is 5.

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Detailed Solution

The water level will increase till the rate of volume going out of the hole is equal to rate of volume poured inside the tank

$\begin{array}{l} 10^{- 4} m^{3} / s = 10^{- 4} v \Rightarrow v = 1 m / s \\ \Rightarrow \sqrt{2 gh} = 1 \Rightarrow 2 \times 10 \times h = 1 \\ h = \frac{1}{20} m = 5 cm \end{array}$

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