A solid sphere of uniform density and radius `R` applies a gravitational force of attraction equal to `F_(1)` on a particle placed at `P`, distance `2R` from the centre `O` of the sphere. A spherical cavity of radius `R//2` is now made in the sphere as shown in figure. The particle with cavity now applies a gravitational force `F_(2)` on same particle placed at `P`. The radio `F_(2)//F_(1)` will be

Explanation

`F_(1)=(GMm)/(4R^(2)), F_(2)=` force due to whole sphere - force due to the sphere forming the cavity
`=(GMm)/(4R^(2))-(GMm)/(18 R^(2))implies (7 GMm)/(36 R^(2))" ":. F_(2)/F_(1)=7/9`