Find the relation in the accelerations of the three masses shown in fig.

Explanation

(a) Length of the string between A and D will remain the same.
For this `(a_(1)-a_(4))+(a_(2)-a_(4))=0`...(i)
`implies a_(1)+2a_(2)-2a_(4)=0`

Length of the string from E to C will remain the same.
`a_(4)+a_(3)=0 implies a_(4)=-a_(3)` ...(ii)
From eq. (i) and (ii), `a_(1)+2a_(2)+2a_(3)=0`
(b) `(a_(1)+a_(2))+(a_(1)+a_(3))+a_(3)=0`
`implies 2a_(1)+a_(2)+2a_(3)=0`.