Discussion
Two objects of masses 1 kg and 2 kg are moving towards each other with accelerations 2 \(ms^{-2}\) and 3 \(ms^{-2}\) respectively on a smooth horizontal surface. The acceleration of centre of mass of the system is
Answer: A
The centre of mass accelerates at \(\frac{4}{3}\) m s-2 in the direction of acceleration of the 2 kg mass.
Take the 1 kg mass's acceleration as positive. Moving towards each other, the 2 kg mass accelerates the opposite way:
\[ \begin{aligned} a_{cm} &= \frac{m_{1}a_{1} + m_{2}a_{2}}{m_{1} + m_{2}} \\ &= \frac{1(2) + 2(-3)}{3} = -\frac{4}{3}\ \text{m s}^{-2} \end{aligned} \]
The negative sign puts it along the 2 kg mass's acceleration. Adding the two terms without the opposite sign gives \(\frac{8}{3}\), and \(\frac{2}{3}\) comes from swapping the masses.
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