99 Percentile Qs Bank for JEE MainPhysicsMechanical Properties of Fluids
On heating water, bubbles beings formed at the bottom of the vessel detach 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 detach is (density of water is ρ )
Options
- AR 2 2 ρ 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 2 ρ w g 3 T
Step-by-step solution
Forces acting on the bubble are: a Buoyant force in upward direction B = ρ w V g ⇒ B = ρ w 4 3 π R 3 g     … 1 , where, ρ w = density of water. b Force due to surface tension. If we consider an elemental length d l at bottom contact, then force due to surface tension is d F = T d l along the tangent to surface & perpendicular to d l . Clearly d F cos θ components on two diametrically elements cancel out & d F sin θ components add up. ∴ Net force due to surfa