A large cylindrical vessel filled with a liquid upto a certain height is empited by a horizontal capillary tube, fitted to its base. Find the ratio of time taken to empty the tank by one half, to the next one fourth

# A large cylindrical vessel filled with a liquid upto a certain height is empited by a horizontal capillary tube, fitted to its base. Find the ratio of time taken to empty the tank by one half, to the next one fourth

1. A

$\sqrt{2}:1$

2. B

$1:\sqrt{3}$

3. C

$\sqrt{3}:1$

4. D

1:1

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### Solution:

From the question,

$\frac{{\mathrm{t}}_{1}}{{\mathrm{t}}_{2}}=\frac{\sqrt{\mathrm{h}}-\sqrt{\frac{\mathrm{h}}{2}}}{\sqrt{\frac{\mathrm{h}}{2}}-\sqrt{\frac{\mathrm{h}}{4}}}=\frac{\sqrt{\mathrm{h}}\left[1-\frac{1}{\sqrt{2}}\right]}{\sqrt{\frac{\mathrm{h}}{2}}\left[1-\frac{1}{\sqrt{2}}\right]}=\frac{\sqrt{2}}{1}$

$\therefore {\mathrm{t}}_{1}:{\mathrm{t}}_{2}=\sqrt{2}:1$

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