Question

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

Answer 1

Let the mass of the needle be m. As the liquid surface is distorted, the surface tension forces acing on both sides of 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
$\sum F_y=Fcos\theta +Fcos\theta -mg=0$
This gives m = $\frac{2Fcos\theta }{g}$
where F = TlThen m = $\frac{2Tlcos\theta }{g}$
For m to be maximum, cos $\theta$ = 1
Hence, $m_{max}=\frac{2Tl}{g}$