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Question

There is a hole at the side-bottom of a big water tank. The area of the hole is $$2\ mm^{2}$$. Through it, a pipe is connected. The upper surface of the water is $$5\ m$$ above the hole. The rate of flow of water through the pipe is ( in $$m^{3}s^{-1}$$) ( $$g= 10 \ ms^{-2}$$)


A
4×105
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B
4×105
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C
4×106
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D
28×106
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Solution

The correct option is C $$4 \times 10^{-5}$$
Velocity of water at the side bottom hole $$=\sqrt{2gh}$$$$=\sqrt{2 \times 10 \times 5}=10 \ m/s$$
Area of hole = $$4 mm^{2}= 4 \times 10^{-6}\ m^{2}$$
So, rate of flow of water through pipe = $$4 \times 10^{-6} \times 10 \ m^{3}/s$$$$=4  \times 10^{-5} \ m^{-3}/s$$

Physics

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