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# Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by which of the following options?A)B)C) D)

Last updated date: 15th Jun 2024
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Hint The gravitational acceleration inside the surface of the Earth is linearly proportional to the radius while outside the surface of the Earth it falls off with the inverse square of the distance. Use the formula of gravitational acceleration to determine the graph of gravity inside and outside the surface of the Earth.

Formula used Gravity inside the surface of Earth: $g = \dfrac{{GMr}}{{{R^3}}}$ where $G$ is the gravitational constant, $M$ is the mass of the Earth, $r$ is the distance from the centre of the Earth and $R$ is the radius of Earth.
Gravity outside the surface of Earth: $g = \dfrac{{GM}}{{{R^2}}}$

$\Rightarrow g = \dfrac{{GMr}}{{{R^3}}}$
$\Rightarrow g = Ar$ where $A = GM/{R^3}$ which is the equation of a line. So the gravitational acceleration inside the surface of the Earth increases linearly with $r$ so the possible choices are (B) and (C).
$\Rightarrow g = \dfrac{{GM}}{{{R^2}}}$
Since outside the surface of the Earth, the distance from the centre of the Earth is $R$, the gravity falls off with the inverse square of the distance which is shown in option (C) from option (B) and (C).