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Question

A metallic wire of density 'd' floats in a fluid of surface tension T. the maximum radius of the wire so that it may not sink is? Assume that the surface of fluid is vertical at the points of contact with the metal wire.


A

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B

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C

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D

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Solution

The correct option is B


Let the radius of the wire be 'r'.

Following figure shows side view of the wire lying on the surface of fluid in consideration.

Let the length of the wire be 'L'

Here F = force due to surface tension =T×L

As there are two surfaces of fluid in contact with the wire as shown in above figure

Hence, 2TL = mg - - - - - - (1)

Now, Density =massvolume
mass=d×πr2×L
from (1),2TL=dπr2Lg
r=(2Tπdg)1/2
Note that this expression is independent of length of the wire.

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