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Question

# While heating water, bubbles begin to form at the bottom of the vessel. After a while, they detach and rise. Consider a bubble to be a sphere of radius R and making a circular contact of radius r with the bottom of the vessel. Here, r<<R, the surface tension of water is T, and density of water is ρw. The value of r, just before the bubble detaches is,

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 A R2√2ρwg3TLet us draw the situation of the bubble. As the bubble just detaches from the surface, Buoyant force = surface tension force 43πR3ρwg=∫T×dlsinθ (ρw)(43πR3)g=(T)(2πr)sinθ Here, sinθ=rR (ρw)(43πR4)g=(T)(2πr2) Solving the above equation, we get, r=√2ρwR4g3T=R2√2ρwg3T Hence, (A) is the correct answer.

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