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

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$\frac{I_{1}}{I_{2}} = \frac{r_{2}^{2}}{r_{1}^{2}} if r_{1} > R and r_{2} > R$

$\frac{I_{1}}{I_{2}} = \frac{r_{1}}{r_{2}} r_{1} > R and r_{2} > R$

$\frac{I_{1}}{I_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} if r_{1} < R and r_{2} < R$

$\frac{I_{1}}{I_{2}} = \frac{r_{1}}{r_{2}} if r_{1} < R and r_{2} < R$

answer is A, B.

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Detailed Solution

$I = \frac{GM}{r^{2}} If r > R & I = \frac{GM}{R^{3}} r, if r < R$

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