Two blocks of mass M and 3M are connected by a light chord which passes over a light frictionless pully. the blocks are released at the same height at t=0. What is the magnitude of acceleration of the centre of mass of the two block system?
I got the answer as g/4 but the answerkey show as g/2. Which is correct? Please explain

Question

Two blocks of mass M and 3M are connected by a light chord which passes over a light frictionless pully. the blocks are released at the same height at t=0. What is the magnitude of acceleration of the centre of mass of the two block system?
I got the answer as g/4 but the answerkey show as g/2. Which is correct? Please explain

aravindg · Answer

Could you show your attempt with the steps included? I can debug it for you. Please also show the free body diagrams.

anonymous · Answer

Dear AravindG,
My attempt was :-
Let T be tension and a be acceleration,
then, 3Mg - T = 3Ma .....(1)
         T - Mg  = Ma   .....(2)
adding 1&2 above,
         2Mg = 4Ma
a = g/2 ( acceleration of each block)
Net downward force = 3Ma - Ma = 2Ma
therefore, 
acceleration of center of mass = 2Ma/4M = a/2 = g/4

Please do correct me,
Thanks!

michele_laino · Answer

hint:
here are the equations of motion:
$$\huge  \left\{ \begin{gathered}
  \tau  - Mg = Ma \hfill \
  \tau  - 3Mg =  - 3Ma \hfill \ 
\end{gathered}  \right.$$
|dw:1450958354599:dw|
please, solve such system for acceleration $a$