A) \[{{r}^{2}}\]
B) \[{{r}^{3}}\]
C) \[{{r}^{6}}\]
D) \[{{r}^{4}}\]
Correct Answer: D
Solution :
Gravitational force acting between the spheres, \[F=G\frac{m\cdot m}{{{(2r)}^{2}}}\] \[=\frac{G\cdot \frac{4}{3}\pi {{r}^{3}}\times {{\rho }_{1}}\times \frac{4}{3}\times \pi {{r}^{3}}\times {{\rho }_{2}}}{4{{r}^{2}}}\] \[=\frac{4}{9}G{{\pi }^{2}}{{\rho }_{1}}{{\rho }_{2}}{{r}^{4}}\] \[\therefore \] \[F\propto {{r}^{4}}\]
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