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Question

On heating water, bubbles beings formed at the bottom of the vessel detatch and rise. Take the bubbles to the 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).
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A
R2ρwg3T
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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 R2ρwg3T
The bubble will detach if p
Buoyant force surface tension
(2πrT)sinθ=43πR3pwg
T×rR×2πr=43πR3pwg
r2=23R4pwgT
r=R2pwg3T
Answer is A

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