Two speres of radii r and 2r touching each other the force of attraction betweeen them is proportional

Options

A. `r^(6)`
B. `r^(4)`
C. `r^(2)`
D. `r^(-2)`

Answer

D

Explanation

`F=(Gm_(1)m_(2))/(r+2r)^(2)=(Gm_(1)m_(2))/(9r^(2))`
i.e `F prop r^(-2)`
Note that `F prop r^(4)` by taking `m=4/3 pi r^(3) p` and then `F prop (r^(3)r^(3))/(r^(2))`
`F prop r^(4)` is not correct because the gravitational law obeys inverse square law and is not related with densities