question_answer

Two metal spheres of equal radius r are touching each other. The force of attraction F between them is

A) \[F\propto {{r}^{4}}\]                      

B)  \[F\propto {{r}^{6}}\]

C)  \[F\propto {{r}^{2}}\]              

D)         \[F\propto \frac{1}{{{r}^{2}}}\]

Correct Answer: A

Solution :

 Force of attraction,                 \[F=\frac{G{{\left( \frac{4}{3}\pi {{r}^{3}}d \right)}^{2}}}{{{(2r)}^{2}}}\] where, \[d=\]density of the sphere \[\therefore \]  \[F=\frac{4}{9}{{\pi }^{2}}{{d}^{2}}\times {{r}^{4}}\] \[\Rightarrow \]               \[F=\alpha \,\,{{r}^{4}}\]