A metal wire of density d floats, in a liquid of surface tension σ, in the horizontal position. The maximum radius of the wire so that it may not sink is

Question

A metal wire of density d floats, in a liquid of surface tension σ, in the horizontal position. The maximum radius of the wire so that it may not sink is (A) √(2 σ/π d g) (B) √(3 σ/π d g) (C) √(5 σ/π d g) (D) √(7 σ/π d g)

Tardigrade Admin · Accepted Answer

σ ⋅(2 l)=(π r2 ⋅ l) d ⋅ g ⇒ r=√(2 σ/π d g)

Q. A metal wire of density $d$ floats, in a liquid of surface tension $σ,$ in the horizontal position. The maximum radius of the wire so that it may not sink is

$\frac{2 σ}{π d g}$

$\frac{3 σ}{π d g}$

$\frac{5 σ}{π d g}$

$\frac{7 σ}{π d g}$

$σ \cdot (2 l) = (π r^{2} \cdot l) d \cdot g$
$\Rightarrow r = \frac{2 σ}{π d g}$

Q. A metal wire of density d floats, in a liquid of surface tension σ, in the horizontal position. The maximum radius of the wire so that it may not sink is

πdg2σ​​

πdg3σ​​

πdg5σ​​

πdg7σ​​