Question 30: Gravitation

Question

Starting from the centre of the earth having radius $$R$$, the variation of $$g$$ (acceleration due to gravity) is shown by

Accepted Answer

Acceleration due to gravity at a depth $$d$$ below the surface of the earth is given by
$$\begin{aligned}
g_{	ext {depth }} & =g_{	ext {surface }}\left(1-\frac{d}{R}ight) \
& =g_{	ext {surface }}\left[\frac{R-d}{R}ight]=d_{	ext {surface }}\left(\frac{r}{R}ight)
\end{aligned}$$
Also, for a point at height $$h$$ above surface,
$$g_{	ext {height }}=g_{	ext {surface }}\left[\frac{R^2}{(R+h)^2}ight]$$
Therefore, we can say that value of $$g$$ increases from centre to maximum at the surface and then decreases as depicted in graph (b).

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Gravitation

Starting from the centre of the earth having radius $R, the variation of g$ (acceleration due to gravity) is shown by

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