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

A

$$R$$

B

$$R^{3}$$

C

$$\frac{1}{R}$$

D

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