Correct Answer - Option 2 : M/2 and M/2
Let m1 = m, m2 = M – m
Force of gravitation between the two parts when they are placed distance r apart –
\(F = \frac{{Gm\left( {M - m} \right)}}{{{r^2}}} = \frac{G}{{{r^2}}}\left( {Mm - {m^2}} \right)\)
Differentiating w.r.to m we get,
\(\frac{{dF}}{{dm}} = \frac{G}{{{r^2}}}\left( {M - 2m} \right)\)
For F to be maximum, \(\frac{{dF}}{{dM}} = 0 \Rightarrow m = \frac{M}{2}\)
\({m_1} = \frac{M}{2}\;and\;{m_2} = \frac{M}{2}\)
