A metallic wire of density ρ 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 θ =0° )

Question

A metallic wire of density ρ 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 θ =0° ) (A) √(2 T/π ρ g) (B) √(4 T/π ρ g) (C) √(T/π ρ g) (D) √(T ρ /π g)

Tardigrade Admin · Accepted Answer

2Tlcosθ =mg 2Tlcosθ =π r2lρ g For maximum radius, cosθ =1 ∴ r=√(2 T/π ρ g)

Q. A metallic wire of density $ρ$ 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 $θ = 0^{\circ}$ )

$\frac{2 T}{π ρ g}$

$\frac{4 T}{π ρ g}$

$\frac{T}{π ρ g}$

$\frac{Tρ}{π g}$

$2 Tl cos θ = m g$
$2 Tl cos θ = π r^{2} lρ g$
For maximum radius, $cos θ = 1$
$∴ r = \frac{2 T}{π ρ g}$

Q. A metallic wire of density ρ 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 θ=0∘ )

πρg2T​​

πρg4T​​

πρgT​​

πgTρ​​