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A sphere of mass M and radius $R_{2}$ has a concentric cavity of radius $R_{1}$ as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as ( $0 \leq r \leq \infty$ ) (mass distribution is uniform)

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Detailed Solution

$F = 0$ when $0 \leq r \leq R_{1}$
because intensity is zero inside the cavity.
F increase when $R_{1} \leq r \leq R_{2}$ as $F \propto \frac{r^{3} - R_{1}^{3}}{r^{2}}$
$F α \frac{1}{r^{2}}$ when $r > R_{2}$

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