On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubble

Question

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)

Accepted Answer

When the bubble gets detached,
Buoyant force = force due to surface tension
∫ T × dl sin θ = π R³ ρ_wg
⇒ T × 2πr × π R³ ρ_wg
⇒ r² =
⇒ r = R²

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