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

Options

A. `2pirT=w`
B. `2pirT costheta-w`
C. `2pirT costheta+w`
D. `w-2pirT costheta`

Answer

C

Explanation

Surface tension force on liquid is downwards. But on the disc it is upwads. In the figure, `F=`Surface tension force
`=Tl cos theta =T(2 pi r)costheta`
`U=upthrust=omega`
`W=`weight of disc
For equilibrium of disc,
`W=U+F=omega+2piTr costheta`.