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Question

# On heating water, bubbles being 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 ρw)

A
R22ρwg3T
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B
R2ρwg6T
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C
R2ρwgT
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D
R23ρwgT
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Solution

## The correct option is B R2√ρwg6T The bubble will detach if, Buoyant force≥ surface tension force 43πR3ρwg≥∫T(dlsinθ) ρw43πR3g≥T ⋅2πrsinθ Here, sinθ=rR Solving, r=√2ρwR4g3T=R2√2ρwg3T Hence, option (B) is correct.

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