A system consists of two point masses, A and B of masses 1 kg and 2 kg respectively. At an instant the kinetic energy of A with respect to the centre of mass is 2 joules and the velocity of centre of mass is 2 m/s. The kinetic energy of the system at this instant is:

KEA/CM=12⋅1⋅vA/CM2= 2 J=vA/CM2⇒VA/CM=2m/sVA→-Vcm→=2i^VA→=Vcm→+2i^=2i^+2i^=4i^ Let Com move towards +ve x-direction.  Then, V→A/CM=2i^VB→-Vcm→=V→B/CMi^-2i^=V→B/CM⇒ vB/CM=−i^  Use ;v→CM=m1v→1+m2v→2m1+m2⇒2i^=1(4i^)+2VB→1+2⇒VB→=i^ ∴ KEsystem =12⋅1.2i^+v→CM2+12⋅2−i^+V→CM2=124+VCM2+2.2i^⋅V→CM+12⋅2⋅1+vCM2−2i^V→CM=2+2+2i^V→CM+1+4−2i^⋅V→CM=9J