Variation of g

Question

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

Easy

Solution

For a point inside the earth i.e. r < R

$E=-\frac{GM}{{R}^{3}}r$

where M and R be mass and radius of the earth respectively. At the centre, r = 0

$\therefore \phantom{\rule{1em}{0ex}}E=0$

For a point outside the earth i.e. r > R,

$E=-\frac{GM}{{r}^{2}}$

On the surface of the earth i.e. r = R

$E=-\frac{GM}{{R}^{2}}$

The variation of E with distance r from the centre is as shown in the figure.

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