Discussion Forum



1)

A metal wire of density $\rho$  floats on a water surface horizontally. If it is NOT to  sink in water , then maximum radius  of wire is proportional to (where, 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:

Option A

Explanation:

Given, density of metal wire = $\rho$

 The 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= Tl ......(i)

 Also, f= mg  .......(ii)

 From, Eqs. (i) and (ii), we get

Tl= mg

 Tl= v$\rho$ g          [ $\because Density (\rho)=\frac{m}{v}$]

  $Tl= \pi r^{2}l\rho g$

$r^{2}=\frac{T}{\pi \rho g}\Rightarrow r=\sqrt{\frac{T}{\pi \rho g}}$