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 1 ρ d ρ d t is constant. The velocity v of any point on the surface of…

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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 1 ρ d ρ d t is constant. The velocity v of any point on the surface of the expanding sphere is proportional to

Aicharya · Accepted Answer

$ho = \frac{m}{v} = \frac{3m}{4\pi R^3}$ $\Rightarrow \frac{1}{ho} \frac{dho}{dt} = -\frac{3}{R} \frac{dR}{dt}$ Since $\Rightarrow \frac{1}{ho} \frac{dho}{dt}$ is constant $	herefore \frac{dR}{dt} \propto R$

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is…

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