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Spheres of the same metarial and same ra...

Spheres of the same metarial and same radius `r` are touching each other. Show that grevitational force between them is directly proportional to `r^(4)`.

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The correct Answer is:
A
`m_(1) = m_(2) =` (volume) (density)
`= ((4)/(3) pi r^(3))rho`
`:. F = (Gm_(1)m_(2))/(r^(2))`
`= (G((4)/(3) pi r^(3))((4)/(3) pi r^(3)) rho^(2))/(r^(2))`
or `F prop r^(4)` Hence proved.
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