Water rises in capillary tube upto a height of 10 cm whereas mercury depresses in it by 3.42 cm. If the angle of contact and density of mercury are 135⁰ and 13.6 gm/cc respectively, then the ratio of the surface tension of water and mercury will be nearly

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5 : 16

13 : 2

2 : 13

16 : 5

answer is D.

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Detailed Solution

We know that factors cause a capillary tube to rise or fall is given,

$h = \frac{2 T \cos θ}{r ρ g}$

hence,

$h_{water} = \frac{2 T_{water}}{ρ_{water} gr}$

$h_{Hg} = \frac{2 T_{Hg} \cos 45^{ο}}{ρ_{Hg} gr}$

$\frac{T_{water}}{T_{Hg}} = \frac{h_{water}}{h_{Hg}} \times \frac{ρ_{water}}{ρ_{Hg}} \times \cos 45^{\circ}$

$\frac{T_{water}}{T_{Hg}} = \frac{10}{3.42} \times \frac{1}{13.6} \times \frac{1}{\sqrt{2}} = \frac{2}{13}$

Hence the correct answer is 2:13.

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