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 the figure. A particle of mass `m'` is placed on the line joining the two centres at 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

`rltxlt2r`

Options

A. `(Gm m')/(4(x-x)^2)`
B. `Gm m'((x-r))/(r^3)`
C. `(Gm m'R)/((x-r)^2)`
D. `(2Gm m')/((x-r)^2)`

Answer

B

Explanation

When 2r < x < 2R then the force will be due to sphere only.
`F=(Gm m')/((x-r)^2)`