Explain the variations of acceleration due to gravity inside and outside the Earth and draw the graph.

(N/A) $1$. Inside the Earth $(r < R_E)$: The acceleration due to gravity at a distance $r$ from the center is given by $g(r) = \frac{4}{3} \pi G \rho r$,where $\rho$ is the density of the Earth. Since $\frac{4}{3} \pi G \rho$ is constant,we have $g(r) \propto r$. This means $g$ increases linearly as we move from the center to the surface.
$2$. Outside the Earth $(r > R_E)$: The acceleration due to gravity at a distance $r$ from the center is given by $g(r) = \frac{GM}{r^2}$. Thus,$g(r) \propto \frac{1}{r^2}$. This means $g$ decreases as the inverse square of the distance from the center.
$3$. At the surface $(r = R_E)$: The value of $g$ is maximum,given by $g = \frac{GM}{R_E^2}$.
The graph shows $g(r)$ on the y-axis and $r$ on the x-axis,illustrating the linear increase inside the Earth and the inverse-square decrease outside the Earth.