Two concentric shells of masses `M_(1)` and `M_(2)` are having radii `r_(1)` and `r_(2)`. Which of the following is the correct expression for the gravitational field on a mass `m`?

Options

A. `F=(G(M_(1)+M_(2)))/(r^(2))`, for `rltr_(1)`
B. `F=(G(M_(1)+M_(2)))/((r^(2))`, for `rltr_(2)`
C. `F=(GM_(2))/(r^(2))`, for `r_(1)ltrltr_(2)`
D. `F=GM_(1)/(r^(2))`, for `r_(1)ltrltr_(2)`

Answer

C

Explanation

Gravitational field inside a shell is zero, but for points outside it, the shell behaves as if whole of its mass is concentrated at its centre. Hence, for a point lying in between the shells there will be a field only due to the inner shell `(=GM_(2)//r^(2))` because the point will be an external point for the inner shell but internal for the outer shell.