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Which graph best represents the variation of acceleration due to gravity g with distance from the centre of the Earth (R = Earth's radius)? The correct behaviour is described by which option?

1. g increases linearly from 0 at the centre to a maximum at r = R, then decreases as 1/r² beyond R.
2. g is constant inside and decreases as 1/r outside.
3. g decreases linearly inside and increases outside.
4. g is maximum at the centre and decreases linearly to zero at the surface.

Correct answer: g increases linearly from 0 at the centre to a maximum at r = R, then decreases as 1/r² beyond R.

Solution

Inside the Earth (assumed uniform density), only the mass within radius r contributes, giving g proportional to r — so g rises linearly from 0 at the centre to its maximum at the surface r = R. Outside the Earth, g = GM/r² decreases as 1/r². Hence the correct graph rises linearly to a peak at r = R and then falls off as 1/r².

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