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`.

Options

A. `(2GMm')/((x-r)^(2))+(Gmm')/((x+r)^(2))`
B. `(Gmm')/(2x(x-R)^(2))+(2Gmm')/((x-r)^(2))`
C. `(Gmm')/((x+R)^(2))+(Gmm')/((x+r)^(2))`
D. `(GMm')/((x-R)^(2))+(Gmm')/((x-r)^(2))`

Answer

D

Explanation

When `2rltxlt2R`
then the force will be due to sphere only.
`F=(Gmm')/((x-r)^(2))`
When `xgt2R`.
the sphere and the shell both will contribute to the
`f_("sphere")=(GMm')/((x-r)^(2))`
`F_("shell")=(GMm')/((x-R)^(2))`
`F=(GMm')/((x-R)^(2))+(GMm')/((x-r)^(2))`