Find the maximum possible mass of a greased needle floating on water surface.

Explanation

Let the mass of the needle be `m`. As the liquid surface is distorted, the surface tension forces acing on both sides o the needle make an angle `theta` say, with vertical. Since the forces acting on the needle are `F,F` and `mg`, resolving the forces vertically for its equilibrium, we have
`sumF_(Y)=costheta+Fcostheta-mg=0`
This gives `m=(2Fcostheta)/g`
where `F=Tl`
Then`m=(2Tlcostheta)/g`
For `m` to be maximum `costheta=1`
Hence `m_("max")=(2Tl)/g`