Mass m is split into two parts m and (M-m), which are then separated by a certain distance. What ratio (m/M) maximies the gravitation force between the parts.

Explanation

If r is the distance m and (M-m), the gravitation force will be
`F = G(m(M-m))/(r^(2)) = (G)/(r^(2)) (mM-m^(2))`
For F to be maximum dF/dm = 0 as M and r are constants.
i.e., `(d)/(dm)[(G)/(r^(2))(mM-m^(2))] = 0` i.e., `M - 2m = 0`
[as `G//r^(2) != 0]`
or (m/M) = (1/2), i.e., the force will be maximum when the parts are equal.