Two concentric spherical shells have masses `M_(1), M_(2)` and radii `R_(1), R_(2)(R_(1) lt R_(2))`. The force exerted by this system on a particle of mass m. If it is placed at a distance `((R_(1)+R_(2))/(2))` from the centre.

Explanation

The gravitational force on .m. due to the shell of `M_(2)` is zero. The gravitational force on .m. due to the shell of `M_(1)` is given by
`=(GM_(1)m)/((R_(1)+R_(2))/(2))^(2) = (4GM_(1)m)/((R_(1)+R_(2))^(2))`