In the arrangement shown in Figure, `m_A=2kg` and `m_B=1kg`. String is light and inextensible. Find the acceleration of centre of mass of both the blocks. Neglect friction everywhere.

Answer

g/9 downwards

Explanation

`a=((m_(2)-m_(1))/(m_(1)+m_(2)))g=((2-1)/(2+1))g=(g)/(3)`
`a_(CM)=(m_(A)a_(A)+m_(B)a_(B))/(m_(B)+m_(B))=(2(-a)+1(a))/(2+1)=-(a)/(3)`
`rArra_(CM)=-(g)/(9)=(g)/(9)`downwards