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On heating water, bubbles being formed at the bottom of the ve

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Solving time: 3 mins

On heating water, bubbles being formed at the bottom of the vessel detatch 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 detatch is (density of water is $ρ$ )

(a) $R^{2} \frac{ρ _{w} g}{3 T}$
(b) $R^{2} \frac{ρ _{w} g}{6 T}$
(c) $R^{2} \frac{ρ _{w} g}{T}$
(d) $R^{2} \frac{3 ρ _{w} g}{T}$

Views: 5,187 students

Updated on: May 11, 2022

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2014

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Owen Discussed

On heating water, bubbles being formed at the bottom of the vessel detatch 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 detatch is (density of water is

ρ

)

(a)

R^{2} \frac{ρ _{w} g}{3 T}

(b)

R^{2} \frac{ρ _{w} g}{6 T}

(c)

R^{2} \frac{ρ _{w} g}{T}

(d)

R^{2} \frac{3 ρ _{w} g}{T}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Exp. (*)
The bubble will detach, if Buoyant force

\geq

Surface tension force
Solution Image

i.e.,

\frac{4}{3} π R^{3} ρ_{w} g \geq \int T \times d l sin θ

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

sin θ = \frac{r}{R}

Solving,

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

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Question Text	On heating water, bubbles being formed at the bottom of the vessel detatch 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 detatch is (density of water is $ρ$ ) (a) $R^{2} \frac{ρ _{w} g}{3 T}$ (b) $R^{2} \frac{ρ _{w} g}{6 T}$ (c) $R^{2} \frac{ρ _{w} g}{T}$ (d) $R^{2} \frac{3 ρ _{w} g}{T}$
Updated On	May 11, 2022
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	409
Avg. Video Duration	6 min

Text solutionVerified

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