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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 R22ρwg3T
Let 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=R22ρwg3T

Hence, (A) is the correct answer.

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