P is a point on the axis of a ring centered at O. The gravitational field at P does not change its magnitude but changes direction by $90°$ when a spherical shell of same mass and same radius as the ring is placed in the region with centre at O’. Then,

Filed at axial point is axial and towards centre O. 

Let $\overline{g}$ due to ring and $\overline{g}$’ due to shell 

Resultant = g at $90°$  to g can only be if angle between $\overline{g}$’ and $\overline{g}$is obtuse as below.

$\Rightarrow {\mathrm{g}}^{\mathrm{\prime }}=\sqrt{2}\mathrm{g}$

If P lies within the shell, g’ will be zero$\Rightarrow$Resultant will be same as $\overline{g}$. Hence P lies on or outside shell.

$\Rightarrow {\mathrm{O}}^{\mathrm{\prime }}\mathrm{P}\ge \mathrm{R}$