Question 410: Gravitation

Question

The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below
The correct figure is
![](https://neetcare-image.cdn.examgoal.net/7kexsk7dvpofe/645e8fc2-12da-4c4d-97c2-53213c5d6d95/8d8394a0-5e65-11ea-a92e-65ddcab57d18/file-7kexsk7dvpoff-500w.jpg)

Accepted Answer

The acceleration due to gravity at a depth d below surface of earth is
$g' = {{GM} \over {{R^2}}}\left( {1 - {d \over R}} \right) = g\left( {1 - {d \over R}} \right)$
g' = 0  at d = R.
i.e., acceleration due to gravity is zero at the centre of earth.
Thus, the variation in value g with r is
For,  r > R,
$g' = {g \over {{{\left( {1 + {h \over R}} \right)}^2}}} = {{g{R^2}} \over {{r^2}}} \Rightarrow g' \propto {1 \over {{r^2}}}$
Here, R + h = r
For r < R, $g' = g\left( {1 - {d \over R}} \right) = {{gr} \over R}$
Here, $R - d = r \Rightarrow g' \propto r$
Therefore, the variation of g with distance from centre of the earth will be as shown in the figure.
![](https://neetcare-image.cdn.examgoal.net/7kexsk7dvvvwu/b647ef07-3987-41e5-8661-1398a8ebc5fb/3a2686e0-5e66-11ea-a92e-65ddcab57d18/file-7kexsk7dvvvwv-388w.jpg)

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Gravitation

The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below The correct figure is

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