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`.

Answer

A, B

Explanation

At point `A`, field stength due to shell will be zero.
Net field is only due metal sphere. Distance between centre of metal sphere and point `A` is `4R`.
`:. E_(A) = (G(m))/(4R)^(2) = (Gm)/(16 R^(2)`
(ii) At point `B`, net field is due to both, due to shell and due to metal sphere.
`:. E_(B) = (Gm)/(5R)^(2) + (Gm)/(6 R)^(2)`
`= (61 Gm)/(900 R^(2))`