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

Answer

C

Explanation

When `2rltxlt2R`

then the force will be due to sphere only. `F=(Gmm')/((x-r)^(2))` when `xgt2R`

the sphere and shell both will contributed to the `F_("sphere")=(GMm')/((x-r)^(2)) F_("shell")=(GMm')/((x-R)^(2))`
`F=(GMm')/((x-R)^(2))+(GMm')/((x-r)^(2))`.