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Gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsGravitation1 Mark
Question
The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
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Answer

Let us consider the diagram of spherical shell having uniform density (p). $\text{M}=(\text{p})\times\frac{4}{3}\pi\text{R}^3$ Therefore, gravitational force between hollow shell and point mass is$\text{F}=\frac{\text{GMm}}{\text{r}^2}$
where M is the mass of the hollow spherical shell and m is the mass of point mass.Therefore, the mass is distributed on the surface of the sphere only, then F = 0 for $0<\text{r}<\text{R}$ (i.e., force inside the shell is zero)
And $\text{F}=\frac{\text{GM}}{\text{r}^2}$ for $\text{r}>\text{R}$
The variation of F versus r is shown in the diagram. Force is maximum at the surface of shell and it is zero if r tends to infinity.

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