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A uniform metal sphere of radius R and m...

A uniform metal sphere of radius `R` and mass `m` is surrounded by a thin uniform spherical shell of same mass and radius `4R`. The centre of the shell `C` falls on the surface of the inner sphere. Find the gravitational fields at points `A` and `B`.

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The correct Answer is:
A, B
At `P_1` gravitatioN/Al field due to sphere M
`=(GM)/((3a+a)^2)=(GM)/(16a^2)`
`AT P_2` GravitatioN/Al field is due to sphere and shell
=(GM)/((a+4a+a)^2) (GM)/((4+a)^2)`
`=(GM)/(36a^2)+(GM)/(25a^2)`
`=(GM)/a^2(1/36+1/25)`e
(GM)/a^2((25+36)/900)=(61/900)(GM)/a^2`
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