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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