Consider an expanding sphere of instantaneous radius R whose total mass remains constant…

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