Consider a system of two identical particles.

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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

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Explanation:

The acceleration can be written as

a_CM=(m₁ a₁+m₂ a₂) / (m₁+m₂)

For identical particles

m₁=m₂=m

⇒a_CM=(m(0)+m(a)) / (m+m)

⇒a_CM=1/2 a

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