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A thin metal disc of radius r floats on ...

A thin metal disc of radius `r` floats on water surface and bends the surface downwards along the perimeter making an angle `theta` with vertical edge of the disc of the disc. If the disc dispplaces a weight of water `W` and surface tension of water is `T`, then the weight of metal disc is

A

`W- 2piT cos theta`

B

`2piT+W`

C

`2piT cos theta - W`

D

`2pT cos theta + W`

Text Solution

Verified by Experts

The correct Answer is:
D

The force due to S.T acting upwards is given by
F=(S.T) ` xx "length = T cos " theta xx 2 pi r`
` :. ` Weight of the metal disc
= upthrust + force due to S.T
= weight of water displaced +F
` = W +2pir (T cos theta ) `
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