Find the acceleration of center of mass of the blocks of masses `m_(1)` and `m_(2) (m_(1)gt m_(2))` in Atwood's machine :

Explanation

We know from Newton.s laws of motion magnitude of acceleration of each block is
`a=((m_(1)-m_(2))/(m_(1)+m_(2)))g`

Now acceleration of their C.M is
`a_(cm)=(m_(1)a+m_(2)(-a))/(m_(1)+m_(2))`, `a_(cm)=((m_(1)-m_(2))//(m_(1)+m_(2)))a`
`a_(cm)=((m_(1)-m_(2))/(m_(1)+m_(2)))((m_(1)-m_(2))/(m_(1)+m_(2)))g`
`:.` Accleration of centre of mass `a_(cm)=((m_(1)-m_(2))/(m_(1)+m_(2)))^(2)g`