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The surface of water in a water tank of cross section area 750 \mathrm{~cm}^2 on the top of a house is \mathrm{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, \mathrm{\frac{d h}{d t}} is \mathrm{x\times 10^{-3} \mathrm{~m} / \mathrm{s}}. The value of \mathrm{x} will be_______________
 

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

By using equation of continuity
\begin{aligned} & \mathrm{A}_1 \mathrm{v}_1=\mathrm{A}_2 \mathrm{v}_2 \\ & 750 \times 10^{-4} \times \mathrm{v}_1=500 \times 10^{-6} \times 30 \times 10^{-2} \\ & \mathrm{v}_1=20 \times 10^{-4} \mathrm{~m} / \mathrm{sec} \\ & \mathrm{v}_1=2 \times 10^{-3} \mathrm{~m} / \mathrm{sec} \end{aligned}
Given : \frac{\mathrm{dh}}{\mathrm{dt}}=\mathrm{v}=\mathrm{x} \times 10^{-3} \mathrm{~m} / \mathrm{sec}.
Therefore

\mathrm{x}=2

Posted by

sudhir.kumar

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