Which of following graph represents variations of acceleration due to gravity (g) with distance r fr

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7.Gravitation

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Which of the following graph represents the variations of acceleration due to gravity $(g)$ with distance $r$ from the centre of earth?

A

B

C

D

Solution

(a)

$M_e \rightarrow$ Mass of earth

$R_\theta \rightarrow$ Radius of earth

The acceleration due to gravity at a distance $r_1$ from the centre of earth such that $r_1 < R$, is given by $g r_1=\frac{G M}{R^3} r_1$

$\Rightarrow g \propto r$

The acceleration due to gravity at a distance $r_2$ from the centre of earth such that $r_2 > R$, is given by $g r_2=\frac{G M}{r_2^2}$

$\Rightarrow g \propto \frac{1}{r^2}$

Standard 11

Physics

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