# Consider A System Of Two Identical Particles. One Of The Particles Is At Rest And The Other Has An Acceleration A. The Centre Of Mass Has An Acceleration (A)A(B)2A(C)1/2A(D)Zero

$$\vec{a}_{cm} = \frac{m_{1}\vec{a}_{1} + m_{2}\vec{a}_{2}}{m_{1} + m_{2}} —[1]$$

As given in the question

$$m_{1} = m_{2} = m$$ $$a_{1} = 0$$ $$a_{2} = a$$

Now by substituting the values in equation [1], we get

$$\vec{a}_{cm} = \frac{m * 0 + m\vec{a}}{2m}$$ $$\vec{a}_{cm} = \frac{1}{2}\vec{a}$$

Acceleration of centre of mass of a two particles system is$$\frac{1}{2}\vec{a}$$

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