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")/(18R^(2))`
`implies(7"GMm")/(36R^(2))" ":.(F_(2))/(F_(1))=(7)/(9)`