Centre Of Mass

The centre of mass of a system of point particles is the mass-weighted average of their positions, defined by $x_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$. Because the connecting rod is light, only the two end masses contribute to the calculation. Take the 2 kg mass at the origin and the 6 kg mass at $x=1\text{ m}$. Then $x_{cm}=\frac{2(0)+6(1)}{2+6}=\frac{6}{8}=0.75\text{ m}$ measured from the 2 kg end. The value 0.25 m is the distance from the heavier 6 kg mass rather than the lighter one, so it answers a different question. The value 0.50 m would only be correct if the two masses were equal, which they are not. The value 0.60 m comes from incorrectly weighting by length rather than by mass. This is the standard NCERT treatment of the centre of mass of a two-particle system. As a sanity check, the centre of mass must always lie closer to the heavier mass, and 0.75 m is indeed nearer the 6 kg end, confirming the result.