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.
(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