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Question

A $${ 16cm }^{ 3 }$$ volume of water flows per second through a capillary tube of radius r cm and of length 1 cm, when connected to a pressure head of h cm of water. If a tube of the same length and radius r/2 is connected to the same pressure head, find the mass of water flowing per minute through the tube 


A
80 gram/min
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B
70 gram/min
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C
60 gram/min
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D
50 gram/min
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Solution

The correct option is B 60 gram/min
$$V \propto \dfrac{Pr^4}{l}$$
$$\dfrac{v_2}{v_1} = \left( \dfrac{r/2}{r} \right)^4$$
$$\dfrac{v_2}{16} = \dfrac{1}{16}$$
$$v_2 = 1 cm^3 $$per sec
$$v_2 = 60 cm^3 $$per min
Mass of water flowing per minute $$= v_2 \times d \\ = 60 \times 1 = 60 gram/min$$
Hence option 'C' is correct.

Physics

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