question_answer

Two metal spheres of same material and radius r are in contact with each other. The gravitational force of attraction between the spheres is proportional to

A)  \[{{r}^{4}}\]    

B)  \[1/{{r}^{3}}\]  

C)  \[{{r}^{3}}\]                      

D)  \[{{r}^{2}}\]

Correct Answer: A

Solution :

  \[F\propto \frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}},\] from the figure, \[d=2r\] \[\therefore F\propto \frac{\frac{4}{3}\pi {{r}^{3}}\rho \times \frac{4}{3}\pi {{r}^{3}}\rho }{{{(2r)}^{2}}}\Rightarrow F\propto {{r}^{4}}\] CIF density is same.