The variation of acceleration due to gravity ($g$) with distance $r$ from the centre of the Earth is derived as follows:

1. Inside the Earth ($r < R$): Assuming uniform density, $g$ is directly proportional to the distance from the centre. The formula is $g = \frac{GM}{R^3}r$, which implies $g \propto r$. This represents a straight line passing through the origin.
2. At the Surface ($r = R$): The value of $g$ reaches its maximum, $g_{surface} = \frac{GM}{R^2}$.
3. Outside the Earth ($r > R$): The value of $g$ decreases with distance according to the inverse square law. The formula is $g = \frac{GM}{r^2}$, which implies $g \propto \frac{1}{r^2}$. This represents a hyperbolic curve decreasing asymptotically towards zero.

Therefore, the correct graph shows a linear increase up to $r=R$ followed by a curvilinear decrease.