Consider an expanding sphere of instantaneous radius R whose total...

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 $\left(\dfrac{1}{ρ}\dfrac{dρ}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to