a solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m is placed on the line joining the two centers as a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if `a). rltxlt2r, b). 2rltxlt2R and c). xgt2R`.

Explanation

Gravitational field at the place of `m'`
`E=E_(sphere)+E_(shell)`
`=(Gm(x-r))/(r^(3))+0`
`F=m'E=(Gmm'(x-r))/(r^(3))`

Gravitational field at the place of `m'`
`E=E_(sphere)+E_(shell)`
`=(Gm)/((x-r)^(2))+0`
`F=m'E=(Gmm')/((x-r)^(2))`
(c)
Gravitational field at the place of `m'`
`E=E_(sphere)+E_(shell)`
`=(Gm)/((x-r)^(2))+(Gm)/((x-R)^(2))`
`F=m'E=Gm'[m/((x-r)^(2))+M/((x-R)^(2))]`