Question 256: Properties of Matter

Question

The surface of water in a water tank of cross section area $$750 \mathrm{~cm}^{2}$$ on the top of a house is $$h \mathrm{~m}$$ above the tap level. The speed of water coming out through the tap of cross section area $$500 \mathrm{~mm}^{2}$$ is $$30 \mathrm{~cm} / \mathrm{s}$$. At that instant, $$\frac{d h}{d t}$$ is $$x 	imes 10^{-3} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ will be ____________.

Accepted Answer

$\begin{aligned} & \mathrm{AV}=\mathrm{av} \\ & 750 	imes 10^{-4} 	imes\left(\frac{d h}{d t}ight)=\left(500 	imes 10^{-6}ight)\left(30 	imes 10^{-2}ight) \\ & \frac{d h}{d t}=\frac{15 	imes 10^{-5}}{75 	imes 10^{-3}} \\ & =\frac{1}{5} 	imes 10^{-2} \\ & =2 	imes 10^{-3} \mathrm{~m} / \mathrm{s} \\ & 	herefore x=2\end{aligned}$

Properties of Matter

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