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(C) According to Newton's law of gravitation,the initial force between two objects of mass $m$ separated by distance $r$ is given by $F = \frac{Gm^2}{

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$\frac{8}{9}F$

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(C) According to Newton's law of gravitation,the initial force between two objects of mass $m$ separated by distance $r$ is given by $F = \frac{Gm^2}{r^2}$.When one-third of the mass of one object is transferred to the other,the new masses become $m_1 = m - \frac{1}{3}m = \frac{2}{3}m$ and $m_2 = m + \frac{1}{3}m = \frac{4}{3}m$.The new gravitational force $F^{\prime}$ is given by $F^{\prime} = \frac{G m_1 m_2}{r^2}$.Substituting the new masses: $F^{\prime} = \frac{G (\frac{2}{3}m) (\frac{4}{3}m)}{r^2} = \frac{8}{9} \frac{Gm^2}{r^2}$.Since $F = \frac{Gm^2}{r^2}$,we get $F^{\prime} = \frac{8}{9}F$.

Two objects of equal masses placed at a certain distance from each other attract 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

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