Question

A paper disc of radius $R$ from which a hole of radius $r$ is cut out is floating in a liquid of the surface tension $S$. The force on the disc due to the surface tension is:

• A. $S\times 2\pi R$
• B. $S\times 2\pi r$
• C. $S\times 2\pi (R-r)$
• D. $S\times 2\pi (R+r)$

Answer 1

The correct option is D $S\times 2\pi (R+r)$

A water layer tries to minimize its surface area. So force on the disc due to inner water layer would be inside and the same due to outer water layer would also be inside.

So surface tension forces would be additive.

Force = $S\times 2\pi R+S\times 2\pi r$

Force = $S\times 2\pi (R+r)$