Solving Acceleration Problem: Find a3 Differently

[varunKanpur]

I am thinking of finding a3 through another way in this solved question

I am thinking of considering m2 and m1 as one mass but answer in not matching. I couldn't find what I am doing wrong.

Thanx in advance .

 

[Doc Al]

I am thinking of considering m2 and m1 as one mass but answer in not matching. I couldn't find what I am doing wrong.

The problem with treating m1 and m2 as a single system is that the acceleration you'll find (using Newton's 2nd law) will be the acceleration of their center of mass. That acceleration is not the same as the acceleration of the pulley.

If m1 and m2 were fixed together, instead of in relative motion, then you'd be fine. (Obviously, that is not the case here.)