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(A) The gravitational force $F$ on a test mass $m$ is given by $F = mI$,where $I$ is the gravitational field intensity.Case $1$: For points outside th

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$\frac{F_1}{F_2} = \frac{r_1}{r_2}$ if $r_1 < R$ and $r_2 < R$

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(A) The gravitational force $F$ on a test mass $m$ is given by $F = mI$,where $I$ is the gravitational field intensity.Case $1$: For points outside the sphere $(r > R)$:The gravitational field intensity is $I = \frac{GM}{r^2}$.Thus,$F \propto \frac{1}{r^2}$.Therefore,$\frac{F_1}{F_2} = \frac{r_2^2}{r_1^2}$ for $r_1 > R$ and $r_2 > R$.Case $2$: For points inside the sphere $(r The gravitational field intensity is $I = \frac{GMr}{R^3}$.Thus,$F \propto r$.Therefore,$\frac{F_1}{F_2} = \frac{r_1}{r_2}$ for $r_1 Comparing these with the given options,option $A$ is correct.

For a sphere of mass $M$ and radius $R$,if the gravitational forces at distances $r_1$ and $r_2$ from the center are $F_1$ and $F_2$ respectively,then:

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