Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration vector a. The centre of mass has an acceleration

(a) zero 

(b)1/2 vector a

(c) vector a

(d) 2vector a.


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(b) 1/2 vector a.

Explanation: 

Let the distance of CoM from the origin be X. if each particles with mass m be at distances x1 and x2 then 

X= (m*x1+ m*x2)/(m+m) 

Velocity of CoM = V =dX/dt = (v1+ v2)/2 

Acceleration of CoM = dV/dt = (a1+ a2)/2 

since a1 =0 and a2 =a, 

Acceleration of CoM = dV/dt = (0+a)/2 =½a

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