The magnitudes of the gravitational field at distances $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_{1}$ and $F_{2}$ respectively. Then

Question

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Answer 1

Gravitational field inside a sphere of radius $R$ at a distance $r$ is $F = \frac{G M}{R ^{3}} r$

And, outside the sphere, it is $F = \frac{G M}{r ^{2}}$

Therefore, for $r < R$
$\frac{F _{1}}{F _{2}} = \frac{r _{1}}{r _{2}}$

And for $r > R$
$\frac{F _{1}}{F _{2}} = \frac{r _{2} ^{2}}{r _{1} ^{2}}$

Answer 2

Gravitational field inside a sphere of radius $R$ at a distance $r$ is $F = \frac{G M}{R ^{3}} r$

And, outside the sphere, it is $F = \frac{G M}{r ^{2}}$

Therefore, for $r < R$

$\frac{F _{1}}{F _{2}} = \frac{r _{1}}{r _{2}}$

And for $r > R$

$\frac{F _{1}}{F _{2}} = \frac{r _{2} ^{2}}{r _{1} ^{2}}$