JEE Main · 2014 · 06 Apr 2014 · Offline · Fluid Mechanics

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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

ρ_{w}

)

(A) $R^{2} \frac{2 ρ _{w} g}{3 T}$ ✓ Correct
(B) $R^{2} \frac{3 ρ _{w} g}{T}$
(C) $R^{2} \frac{ρ _{w} g}{3 T}$
(D) $R^{2} \frac{ρ _{w} g}{6 T}$

Answer: (A)

Solution

Just before detaching, the upward buoyant force balances the downward vertical pull of surface tension round the contact circle:

\frac{4}{3} π R^{3} ρ_{w} g = (2 π r) T sin θ

, with

sin θ \approx \frac{r}{R}

for

r ≪ R

. Thus

\frac{4}{3} π R^{3} ρ_{w} g = \frac{2 π r ^{2} T}{R} \Rightarrow r = R^{2} \frac{2 ρ _{w} g}{3 T}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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JEE Main · 2014 · 06 Apr 2014 · Offline · Fluid Mechanics

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