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Two particles of mass $2kg$ and $1kg$ are moving along the same line with speeds $2ms-1$ and $5ms^{-1}$ respectively. What is the speed of the centre of mass of the system if both the particles are moving (a) in same direction (b) in opposite direction?
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Here, $m_1 = 2kg, m_2 = 1kg v_1 = 2m/ s, v_2 = 5m/ s, v cm = ? v_1 = 2m/ s, v_2 = -5m/ s, v cm = ?$ Use $\vec{\text{v}}_{\text{cm}}=\frac{\text{m}_1\text{v}_1+\text{m}_2\vec{\text{v}}_2}{\text{m}_1+\text{m}_2}$
  1. $\vec{\text{v}}_{\text{cm}}=\frac{2\times2+1\times5}{2+1}=3\text{ms}^{-1}$
  2. $\vec{\text{v}}_{\text{cm}}=\frac{2\times2-5\times1}{2+1}=-\frac{1}{3}\text{ms}^{-1}$
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