Two concentric spherical shells have masses `m_(1) and m_(2)` and radii `r_(1) and r_(2) (r_(2) gt r_(1))`. What is the force exerted by this system on a particle of mass `m_(3)`. If it is placed at a distance `r(r_(1) lt r lt r_(2))` from the centre ?

Explanation

The outer shell will have no contribution in the gravitational field at point P
`:. E_(P) = (Gm_(1))/(r^(2))`

Thus, force on mass `m_(2)` placed at P is, ltbr? `F = m_(3)E_(P)`
or `F=(Gm_(1)m_(3))/(r^(2))`
The field `E_(P)` and the force F both are towards centre O.