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(A) Let $M_e$ be the mass of the Earth and $R$ be the radius of the Earth.$1$. For a point inside the Earth at a distance $r$ from the center $(r < R)

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(A) Let $M_e$ be the mass of the Earth and $R$ be the radius of the Earth.$1$. For a point inside the Earth at a distance $r$ from the center $(r $g_{in} = \frac{G M_e r}{R^3}$This implies $g \propto r$, which is a linear relationship passing through the origin.$2$. For a point outside the Earth at a distance $r$ from the center $(r \geq R)$, the acceleration due to gravity is given by:$g_{out} = \frac{G M_e}{r^2}$This implies $g \propto \frac{1}{r^2}$, which is a hyperbolic decay curve.At the surface $(r = R)$, the value of $g$ is maximum, $g_{max} = \frac{G M_e}{R^2}$.Comparing this with the given options, the graph that shows a linear increase for $r  R$ is represented by the first graph (Graph $A$).

Which of the following graphs represents the variation of acceleration due to gravity $(g)$ with distance $r$ from the centre of the Earth?

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