Consider the double Atwood's machine as shown in the figure
(a) Whatis acceleration of the masses?
(b) What is the tension in each string?

Explanation

(a) Here the system behaves as rigid system, therefore every part of the system will move with same acceleration. Thus
Applying Newton's law `mg-T=ma`....(i)
`2T-mg=ma`...(ii)
Doubling the first equation and adding
`mg=3 ma rArr` acceleration `a=(1)/(3)g`
(b) Tension in the string `T=m(g-a)=m(g-(g)/(3))=(2)/(3)mg`