Gravitational field intensity

Question

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 $(0\le \mathrm{r}\le \mathrm{\infty})$

Moderate

Solution

$\mathrm{F}=0\text{when}0\le \mathrm{r}\le {\mathrm{R}}_{1}$

because intensity is zero inside the cavity.

F increase when ${\mathrm{R}}_{1}\le \mathrm{r}\le {\mathrm{R}}_{2}$

$\mathrm{F}\propto \frac{1}{{\mathrm{r}}^{2}}\text{when}\mathrm{r}{\mathrm{R}}_{2}$

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