Question

Two concentric shells of mass `m_(1)` and `m_(2)` are situated as shown. Find the force on a particle of mass `m` when the particles is located at `(a) r=r_(1),(b)r=r_(2),(c)r=r_(3)`. The distance `r` is measured from the centre of the shell.

Answer 1

(a) At `A:`
`E_(A)=E_(1)+E_(2)=(Gm_(1))/(r_(1)^(2))+(Gm_(2))/(r_(1)^(2))=(G(m_(1)+m_(2)))/(r_(1)^(2))`
`F=mE_(A)=(G(m_(1)+m_(2)m))/(r_(1)^(2))`
(b) `E_(B)=E_(1)+E_(2)=(Gm_(2))/(r_(2)^(2))+0`
`F=mE_(B)=(Gm_(2)m)/(r_(2)^(2))`
(c) `E_(C)=E_(1)+E_(2)=0`
`F=mE_(C)=0`