In case of system of two-particles of different masses, the centre of mass lies (a) at the mid-point of line joining the two particles. (b) on the line joining the two particles. (c) at one end of the line joining the two particles. (d) on the line perpendicular to the line joining the two particles.

Answer: (b). For two particles, xcm = (m₁ x₁ + m₂ x₂)/(m₁ + m₂) is a weighted average of the two positions. A weighted average of two points always lies on the line joining them, closer to the heavier mass (not at the mid-point unless m₁ = m₂). So the answer is (b) on the line joining the two particles.

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Centre of Mass of Discrete Particles

In case of system of two-particles of different masses, the centre of mass lies

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Answer: (b)

For two particles, $x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$ is a weighted average of the two positions.
A weighted average of two points always lies on the line joining them, closer to the heavier mass (not at the mid-point unless $m_1 = m_2$ ).
So the answer is (b) on the line joining the two particles.

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