JEE Main2014PhysicsMechanical Properties of FluidsActual
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubbles detatch is : (density of water is ρ w )
Options
- AR 2 2ρ w g 3 T
- BR 2 ρ w g 6 T
- CR 2 ρ w g T
- DR 2 3 ρ w g T
Correct answer
A. R 2 2ρ w g 3 T
Step-by-step solution
When the bubble gets detached, Buoyant force = force due to surface tension ∫ T × dl sin θ = 4 3 π R 3 ρ w g ⇒ T × 2 π r × r R = 4 3 π R 3 ρ w g ⇒ r 2 = 2 R 4 ρ w g 3T