Physics - Fluid Question with Solution | TestHub

Let the maximum radius of the wire be $r$.

The weight of the metal wire acting downwards is given by:

$W=\text{Volume}\times \text{density}\times g=(\pi r^{2}L)dg$

The maximum upward force due to surface tension acts along the entire length of the wire on both sides. This occurs when the liquid surface becomes vertical at the points of contact.

$F=2TL$

For the wire to just float and not sink, the upward surface tension force must balance the downward weight of the wire:

$W=F$

$\pi r^{2}Ldg=2TL$

$\pi r^{2}dg=2T$

$r^2=\frac{2T}{\pi dg}$

$r=\sqrt{\frac{2T}{\pi dg}}$

Answer: $\sqrt{\frac{2T}{\pi dg}}$