A meteor of mass M breaks up into two parts. The mass of one part is m. For a given separation r the mutual gravitational force between the two parts will be the maximum if

Mass of the second part = M$-$m. Gravitational force between the two parts is 

$F=\frac{G(M-m)m}{r^2}=\frac{G}{r^2}(Mm-m^2)$

F will be maximum if $\frac{dF}{dm}=0 and \frac{d^{2}F}{d{m}^2} is negative.$

Now, $\frac{dF}{dm}=\frac{G}{r^2}(M-2m)$. Setting $\frac{d F}{d m}=0$, we get     M$-$2m=0 or m =$\frac{M}{2}$.Now

$\frac{d^{2}F}{d{m}^2}=-\frac{2G}{r^2}$, which is negative.

Hence the correct choice is (a)