Two objects of equal masses placed at certain distance from each other attracts each other with a force of $$F$$. If one-third mass of one object is transferred to the other object, then the new force will be

Two objects of equal mass $$m$$ are placed at distance $$d$$ apart. The initial gravitational force is $$F = \frac{Gm^2}{d^2}$$.

Find the new masses after transferring one-third of one object's mass.

One-third mass of one object ($$m/3$$) is transferred to the other.

New mass of first object: $$m - \frac{m}{3} = \frac{2m}{3}$$

New mass of second object: $$m + \frac{m}{3} = \frac{4m}{3}$$

Calculate the new gravitational force.

$$F' = \frac{G \times \frac{2m}{3} \times \frac{4m}{3}}{d^2} = \frac{G \times \frac{8m^2}{9}}{d^2} = \frac{8}{9} \times \frac{Gm^2}{d^2} = \frac{8}{9}F$$

The correct answer is Option C.