First slide

Variation of g

Question

Which graph correctly presents the variation of acceleration due to gravity with distance from the centre of the earth?

Moderate

A
B
C
D

Solution

$g_{d} = g (1 - \frac{d}{g})$
or $g_{d} = g \frac{R - d}{R}$
or $g_{d} = \frac{gy}{R} or g_{d} \propto y$
So, within the Earth, the acceleration due to gravity varies linearly, with the distance from the centre of the Earth. This explains the linear portion OA of the graphs.

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