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A thin metal disc of radius r floats on a liquid surface and bends the surface downwards along the perimeter making an angle $θ$ with vertical edge of the disc. If the disc displaces a weight of liquid w and surface tension of liquid is T, then the weight of metal disc is

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$2 πrT + w$

$2 πrTcosθ - w$

$2 πrTcosθ + w$

$w - 2 πrTcosθ$

answer is C.

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Detailed Solution

Surface tension force on liquid is downwards. But on the disc it is upwards.

In the figure,

F = Surface tension force

$= Tlcosθ = T (2 πr) cosθ$

U =upthrust =w

W =weight of disc

For equilibrium of disc,

$W = U + F = w + 2 π Tr cosθ$

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