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Volume expansion

Consider an expanding sphere of instantaneous radius R whose t

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Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $ρ$ remains uniform throughout the volume. The rate of fractional change in density $(\frac{1}{p} \frac{d ρ}{d t})$ is constant. The velocity $v$ of any point of the surface of the expanding sphere is proportional to

Name: Video solution 1: Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density (p1dtdρ) is constant. The velocity v of any point of the surface of the expanding sphere is proportional to
Uploaded: 2022-10-03T12:45:13.000Z
Duration: 7 min
Description: Video solution 1: Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density (p1dtdρ) is constant. The velocity v of any point of the surface of the expanding sphere is proportional to

SELECT MULTIPLE OPTION

R

\frac{1}{R}

R^{3}

R^{\frac{2}{3}}

Views: 5,221 students

Updated on: Oct 3, 2022

Book:

Mechanics Volume 2 (DC Pandey)

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Michael Discussed

Consider an expanding sphere of instantaneous radius

R

whose total mass remains constant. The expansion is such that the instantaneous density

ρ

remains uniform throughout the volume. The rate of fractional change in density

(\frac{1}{p} \frac{d ρ}{d t})

is constant. The velocity

v

of any point of the surface of the expanding sphere is proportional to

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

(a)

m = \frac{4 π R ^{3}}{3} \times ρ

On taking log both sides, we have

ln (m) = in (\frac{4 π}{3}) + ln (ρ) + 3 ln (R)

On differentiating with respect to time,

0 = 0 + \frac{1}{ρ} \frac{d ρ}{d t} + \frac{3}{R} \frac{d R}{d t}

v = \frac{d R}{d t} = K R \Rightarrow v \propto R

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Question Text	Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $ρ$ remains uniform throughout the volume. The rate of fractional change in density $(\frac{1}{p} \frac{d ρ}{d t})$ is constant. The velocity $v$ of any point of the surface of the expanding sphere is proportional to
Updated On	Oct 3, 2022
Topic	Mechanical Properties of Solids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	192
Avg. Video Duration	7 min

Text solutionVerified

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