The surface of water in a water tank of cross section area 750 cm² 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 mm² is 30 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 2.

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Detailed Solution

$\begin{array}{l} A = 750 \times 10^{- 4} m^{2} \\ a = 500 \times 10^{- 6} m^{2} \\ v = 30 \times 10^{- 2} m / s \\ \frac{dh}{dt} = ? \end{array}$
According to the equation of continuity
$\begin{array}{l} A (\frac{dh}{dt}) = av \\ \frac{dh}{dt} = \frac{av}{A} = \frac{500 \times 10^{- 6} \times 30 \times 10^{- 2}}{750 \times 10^{- 4}} \\ \frac{dh}{dt} = 2 \times 10^{- 3} m / s x = 2 \end{array}$