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Two particles of masses 1 kg and 0.5 kg are moving in the same direction with speeds of 2 m/s and 6 m/s, respectively, on a smooth horizontal surface. The speed of the centre of mass of the system is:

1. 10/3 m/s
2. 10/7 m/s
3. 11/2 m/s
4. 12/3 m/s

Correct answer: 10/3 m/s

Solution

The centre of mass speed is given by $v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$. Substituting the values gives $v_{cm}=\frac{1\cdot2+0.5\cdot6}{1+0.5}=\frac{5}{1.5}=\frac{10}{3}$ m/s.

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