Find the velocity of centre of mass of the system of two moving particles of mass m and 2m, as shown in the figures (i), (ii) and (iii).

Explanation

Referring to the equation `vecv_(cm) = (summ_(1)vecv_(1))/(summ_(1))`
we have, (i) `vecv_(cm) =((m)(2vhati) + (2m)(-vhati))/(m+2m) =vec0`
(ii) `vecv_(cm) =(m(2vhati ) + 2m(vhati))/(m+2m) =(4v)/3 hati`
(iii) `vecv_(cm) = (m(2vhati ) + 2m(vhatj))/(m+2m) =(2v)/3(hati + hatj)`