Question

A metal wire of density $'\rho'$ floats on water surface horizontally. If it is NOT to sink in water then maximum radius of wire is proportional to (T = surface tension of water, g = gravitational acceleration)

• A. $\sqrt{\frac{T}{\pi\rho g }}$
• B. $\sqrt{\frac{\pi\rho g }{T}}$
• C. $\frac{T}{\pi\rho g }$
• D. $\frac{\pi\rho g }{T}$

Answer 1

Answer: (A)

$\sqrt{\frac{T}{\pi\rho g }}$

Answer 2

Given, density of metal wire $=\rho$
Surface tension of water $=T$
If l is the length of the wire and $f$ the total force on either side of the wire, then
$f=T l \,\,\,\,\,\, (i)$
Also, $\,\,\,f=m g \,\,\,\,\, (ii)$
From Eqs. (i) and (ii), we get
$T l=m g$
$T l=v \rho g \,\,\,\,\,\,\left[\because \text { Density }(\rho)=\frac{m}{v}\right]$
$T l=\pi r^{2} / \rho g$
$r^{2}=\frac{T}{\pi \rho g} \Rightarrow r=\sqrt{\frac{T}{\pi \rho g}}$