Question

centre of mass of three particle system of masses 1kg, 2kg, 3kg is (1,1,1) respectively, where should we place a particle of mass 4kg so that centre of mass of entire shifts to (3,3,3)?

Answer 1

Centre of mass is a point where you can put all the combine mass at one place.
so 1,2,3 kg are at 1,1,1 means 6 kg at 1,1,1
here we will take different component X , y , z
so x for 6kg is 1...let for 4 kg be a
hence Xcm = (1(6)+a(4))/(6+4)
Xcm is 3..solving above we get a=34/4=8.5
Similarly for Ycm and Zcm
point will be (8.5,8.5,8.5)