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Water rises to a height of 40 cm in a capillary tube of cross-sectional area A. If the cross-sectional area of tube is made 4A, then height to which water will rise in the capillary tube will be

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80 cm

20 cm

10 cm

40 cm

answer is B.

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Detailed Solution

$\begin{array}{l} h = \frac{2 Tcos θ}{rρg}, r = radius of tube \\ A = {πr}^{2} \\ ∴ h \propto \frac{1}{\sqrt{A}} \\ ∴ \frac{h^{'}}{h} = \frac{\sqrt{A}}{\sqrt{4 A}} = \frac{1}{2} \\ h^{'} = \frac{1}{2} \times 40 = 20 cm \end{array}$

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