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Q.

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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a

w-2πrTcosθ

b

2πrT+w

c

2πrTcosθ+w

d

2πrTcosθ-w

 

answer is C.

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Detailed Solution

Question Image

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

In the figure,

F = Surface tension force 

=Tlcosθ=T(2πr)cosθ

U =upthrust =w

W =weight of disc 

For equilibrium of disc,

W=U+F=w+2πTrcosθ

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