Question

A metallic wire of density $d$ floats in water. The maximum radius of the wire, so that it may not sink is

• A. $\sqrt{2\pi dgT}$
• B. $\sqrt{\frac{2T}{\pi dg}}$
• C. $\sqrt{\frac{\pi dg}{2T}}$
• D. $\sqrt{\frac{2Tg}{\pi d}}$

Answer 1

The correct option is B $\sqrt{\frac{2T}{\pi dg}}$

The wire does not sink if the surface tension force $\left(T\right)$ acting on it balances the weight $\left(mg\right)$ of the wire.
So net force on the wire will be zero.
$\therefore mg=T\cdot 2l$
$\Rightarrow \left(\pi r^{2}ld\right)g=T\cdot 2l$
$\therefore r=\sqrt{\frac{2T}{\pi dg}}$