Question

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R$ = Earth's radius)

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Acceleration due to gravity at a depth $d$ from the earth surface $g=g_o(1-\frac{d}{R})$
Thus distance from earth's centre $x=R-d$ i.e. $d=R-x$
$⟹$ $g=g_o\frac{x}{R}$

Thus acceleration due to gravity increases linearly with the increase in distance from centre of earth.
Acceleration due to gravity at a height $h$ from the earth surface $g=g_o(\frac{R}{R+h}{)}^2$

Thus distance from earth's centre $x=R+h$ i.e. $h=x-R$
$⟹$ $g=g_o(\frac{R}{x}{)}^2$
Thus acceleration due to gravity decreases as $\frac{1}{x^2}$ with the increase in distance from centre of earth.