Explain the variations of acceleration due to gravity inside and outside the earth and draw the graph.
Explain the variations of acceleration due to gravity inside and outside the earth and draw the graph.
In $g(r)=\frac{4}{3} \pi \mathrm{Grp}, \frac{4}{3} \pi \mathrm{Gp}$ is constant.
$\therefore g(r) \propto r$
Means, the gravitational acceleration $(g)$ at a point inside the earth is directly proportional to the distance of that point from the centre of the earth.
And $g(r)=\frac{\text { GM }}{r^{2}}$, where $r \gg>\mathrm{R}_{\mathrm{E}}$ so, $g(r) \propto \frac{1}{r^{2}}$ where $r \gg>\mathrm{R}_{\mathrm{E}} .$ Hence starting from the centre of the earth $g(r)$ increases in directly proportion as $r$ increases and then outside the surface $g(r)$ decreases as inverse square of distance.
The variations in gravitational acceleration with below the surface of earth and above the height from the surface is shown as in figure.
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- [AIIMS 1985]