A bubble having surface tension. T and radius R is formed on a ring of radius $b (b < < R)$ . Air is blown inside the tube with velocity v as shown. The air molecule collides perpendicularly with the will of the bubble and stops. Calculate the radius at which the bubble separates from the ring

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$\frac{8 T}{ρ V^{2}}$

$\frac{16 T}{ρ V^{2}}$

$\frac{4 T}{ρ V^{2}}$

$\frac{10 T}{ρ V^{2}}$

answer is A.

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Detailed Solution

The bubble will separate from the tube when thrust force exerted by the air is equal to the force due to excess pressure.

$F = P A ρ A v^{2} = \frac{4 T}{R} A$

$∴$ $R = \frac{4 T}{ρ v^{2}}$

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