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Question

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75×104 N force due to the weight of the liquid. If the surface tension of water is 6×102 Nm1, the inner circumference of the capillary must be

A
1.25×102 m
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B
0.50×102 m
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C
6.5×102 m
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D
12.5×102 m
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Solution

The correct option is D 12.5×102 m
Let T be the surface tension, θ the angle of contact and R be the radius of capillary tube.

The vertical component of the surface tension force will balance the weight of the liquid column.
Therefore,
Tcos θ×2πR=mg
Since angle of contact, θ=0
T×2πR=mg
2πR=mgT=75×1046×102
2πR=12.5×102 m
Hence the circumference of the capillary tube is 12.5×102 m

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