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# A sphere of mass M and radius $R_2$ has a concentric cavity of radius $R_1$ as shown. The force F exerted by the sphere on a particle of mass m located at a distance r from the center of sphere varies as $(0 < r < \alpha)$

Options are:

$\begin{array}{1 1} a \\ b \\ c \\ d \end{array}$

1) $0 < r< R_1 \qquad F(r)=0$
2) $R_2 < r< R_2 \qquad F(r)=\large\frac{4}{3} $$\pi G\rho m \bigg( r - \large\frac{R_1^3}{r^2}\bigg) 3) R_2 < r< \infty \qquad F(r)=\large\frac{4}{3}$$\pi G\rho m \bigg( \large\frac{R_2^3-R_1^3}{r}\bigg)$
In region 1 - $F=0$
In region 2 - $F$ increase gradually
In region 3 - $F$ decrease gradually