A small point of mass \(m\) is placed at a distance \(2 R\) from the centre ' \(O^{\prime}\) of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is \(\mathrm{F}_1\). A spherical part of radius \(\mathrm{R} / 3\) is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be \(\mathrm{F}_2\). The value of ratio \(\mathrm{F}_1: \mathrm{F}_2\) is _______.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.