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The angle of contact between glass and water is 0^o and it rises in a capillary up to 6 cm when its surface tension is 70 dynes/cm. Another liquid of surface tension 140 dynes/cm, angle of contact 60^o and relative density 2 will rise in the same capillary by

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12 cm

24 cm

3 cm

6 cm

answer is C.

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Detailed Solution

Given,

$T_{1} = 70 dyne / cm, T_{2} = 140 dyne / cm$

$θ_{1} = 0^{°}, θ_{2} = 60^{°}$

$\frac{ρ_{2}}{ρ_{1}} = 2, h_{1} = 6 cm$

The rise in the capillary is , $h = \frac{2 Tcosθ}{ρgr}$

thus from the question,

$\frac{h_{2}}{h_{1}} = \frac{T_{2}}{T_{1}} \times \frac{{cosθ}_{1}}{{cosθ}_{2}} \times \frac{ρ_{1}}{ρ_{2}} \times \frac{r_{1}}{r_{2}}$

$\frac{h_{2}}{h_{1}} = \frac{140}{70} \times \frac{\cos 60^{°}}{\cos 0^{°}} \times \frac{1}{2} \times 1$

$h_{2} = \frac{h_{1}}{2} = 3 cm$

Hence the correct answer is 3cm.

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