Question

A metallic wire of density $\rho $ floats horizontally in the water. The maximum radius of the wire so that the wire may not sink will be (surface tension of water $=T$ and angle of contact $\theta =0^\circ $ )

• A. $\sqrt{\frac{2 T}{\pi \rho g}}$
• B. $\sqrt{\frac{4 T}{\pi \rho g}}$
• C. $\sqrt{\frac{T}{\pi \rho g}}$
• D. $\sqrt{\frac{T \rho }{\pi g}}$

Answer 1

Answer: (A)

$2Tlcos\theta =mg$
$2Tlcos\theta =\pi r^{2}l\rho g$
For maximum radius, $cos\theta =1$
$\therefore r=\sqrt{\frac{2 T}{\pi \rho g}}$