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`.

Answer

(a) `(Gmm'(x-r))/(r^(3))` , (b) `(Gmm')/((x-r)^(2))` , (c ) `(GMm')/((x-R)^(2))+(Gmm')/((x-r)^(2))`