The surface of water in a water tank of cross section area $750 {cm}^{2}$ on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross section area $500 {mm}^{2}$ is $60 cm / s$ . At that instant, $\frac{dh}{dt}$ is $x \times 10^{- 3} m / s$ . The value of x will be .

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answer is 4.

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Detailed Solution

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By continuity equation $A_{1} V_{1} = A_{2} V_{2} =$ volume flow rate
Also, volume flow rate $= A_{1} \frac{d h}{d t}$
So, volume flow rate $= A_{2} V_{2} = A_{1} \frac{d h}{d t} \Rightarrow A_{2} V_{2} = A_{1} \frac{d h}{d t}$
$\begin{array}{r} \Rightarrow 500 \times 10^{- 6} \times 0.60 = 750 \times 10^{- 4} \times \frac{dh}{dt} \\ \Rightarrow \frac{dh}{dt} = 4 \times 10^{- 3} m / s ∵ x = 4 \end{array}$