Question

The material of a wire has a density of $1.4gc{m}^{-3}$. If it is not wetted by a liquid of surface tension 44 dyne $c{m}^{-1}$, then the maximum radius of the wire which can float on the surface of the liquid is:

• A. 0.7 cm
• B. $\frac{10}{7}mm$
• C. $\frac{10}{14}cm$
• D. $\frac{10}{28}cm$

Answer 1

Answer: (B)

$\frac{10}{7}mm$

Let the length and radius of the wire be $l$ and $R$ respectively.

Weight of the wire $W=Mg=\rho \left(\pi R^{2}l\right)g$ (downward)

Upward force on wire due to surface tension $F=T\left(2l\right)$

(Here a factor of 2 comes because the surface tension acts on both sides of wire)

$\therefore$ At equilibrium, $2lT=\rho \pi R^{2}lg$

$⟹$ $2T=\rho \pi R^{2}g$

OR $2\times 44=1.4\times \frac{22}{7}{R}^2\times 980$ $⟹R=\frac{1}{7}$ cm

$⟹R=\frac{10}{7}$ mm