The distance between two bodies `A` and `B` is `r`. Taking the gravitational force according to the law of inverses square of `r`, the acceleration of the body `A` is `a`. If the gravitational force follows an inverse fourth power law, then what would be the acceleration of the body `A`?

Explanation

According to inverse square law, the gravitational force of attraction between two bodies `A` and `b` of masses `m_(1)` and `m_(2)` is,
`F = (Gm_(1) m_(2))/(r^(2))`
Acceleration of body `A`
`= (F)/(m_(1)) = (Gm_(2))/(r^(2)) = a` (Given)
Following inverse fourth power law,
`F' = (Gm_(1) m_(2))/(r^(4))`
Acceleration of body `A`
`= (F')/(m_(1)) = (Gm_(2))/(r^(4)) = (Gm_(2))/(r^(2)) xx (1)/(r^(2)) = (a)/(r^(2))`