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The magnitude of the gravitational field at distance $r_{1}$ and $r_{2}$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_{1}$ and $F_{2}$ respectively then

This question has multiple correct options

A

$(F_{1} / F_{2}) = (r_{1} / r_{2})$ if $r_{1} < R$ and $r_{2} < R$

B

$(F_{1} / F_{2}) = (r_{1} / r_{2})^{2}$ if $r_{1} > R$ and $r_{2} > R$

C

$(F_{1} / F_{2}) = (r_{1} / r_{2})$ if $r_{1} > R$ and $r_{2} > R$

D

$(F_{1} / F_{2}) = (r_{1} / r_{2})^{2}$ if $r_{1} < R$ and $r_{2} < R$

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Solution

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Correct options are A) and B)

$F \propto r (r < R)$
$F \propto \frac{1}{r ^{2}} (r > R)$
$\frac{F _{1}}{F _{2}} = \frac{r _{1}}{r _{2}}$ if $r < R$ and $\frac{F _{1}}{F _{2}} = (\frac{r _{2}}{r _{1}})^{2}$ if $r > R$
Hence (A) and (B) are correct.

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