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. `(2GM m')/((x-r)^2) +(2Gm m')/((x+r)^2)`
B. `(GM m')/(2(x-r)^2)+(2Gm m')/((x-r)^2)`
C. `(GM m')/((x+r)^2)+ (Gm m')/((x+r)^2)`
D. `(GM m')/((x-R)^2) + (Gm m')/((x-r)^2)`

Answer

D

Explanation

When x > 2R, the sphere and the shell both will contribute to the gravitational force

`F_"sphere"=(Gm m')/((x-R)^2) , F_"shell"=(GM m')/((x-r)^2) , F=(GMm')/((x-R)^2)+(Gmm')/((x-r)^2)`