Gravitational Field with Variable Density

Question

The density of a spherical planet of radius $$R$$ varies with the distance $$r$$ from its center according to the function $$\rho(r) = \rho_0 \left(1 - \frac{r^2}{R^2}\right)$$, where $$\rho_0$$ is a constant. Which of the following represents the magnitude of the gravitational field at a distance $$r$$ from the center, for $$r < R$$?

Accepted Answer

$$\frac{4\pi G \rho_0}{3}\left(r - \frac{r^3}{5R^2}\right)$$

Answer

$$(4\pi G \rho_0/3)(r - r^3/R^2)$$

Answer

$$(4\pi G \rho_0/3)r$$

Answer

$$G\rho_0(1 - r^2/R^2)r$$

Gravitational Field with Variable Density

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