Two identical spheres of radius R made of the same material are kept at a distance d apart. Then the gravitational attraction between them is proportional to

Options

A. `F prop (1)/(R^(2))`
B. `F prop R`
C. `F prop R^(4)`
D. `F prop (1)/(R)`

Answer

C

Explanation

Let masses of two balls are `m_(1)=m_(2)=m` (given) and the density be `rho`. Distance between their centres = AB = 2R

Thus, the magnitude of the gravitational force F that two balls separated by a distance 2R exert on each other is
`F=G((m)(m))/((2R)^(2))=G(m^(2))/(4R^(2))=G(((4)/(3)piR^(3)rho))/(4R^(2))`
`:. F prop R^(4)`.