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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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Solution
Let us consider the diagram of a spherical shell having uniform density (ρ).
Mass of the shell = (Density) × (Volume)
`M = (ρ) xx 4/3 πR^3`
Therefore, the gravitational force between the hollow shell and point mass is`F = (GMm)/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 < r < R (i.e., force inside the shell is zero)
And `F = (GM)/r^2 for `r ≥ 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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