Problem: Two masses $A$ and $B$ connected with an inextensible string of length $l$ lie on a smooth horizontal plane. $A$ is given a velocity of $v$ m/s along the ground perpendicular to line $AB$ as shown in the figure. Find the tension in string just after this instant?
Solution: I solved this problem in the Center of Mass frame of reference by getting the velocities of both the masses in C.M frame and applying $T = Mv^2/r$ for one of the bodies. And I got the answer. (as here)
My Question: I am not satisfied with my solution. I am not convinced why I had to solve this problem in C.M frame.
Because mass B is at rest (just after), why isn't it the instantaneous axis of rotation? and then, if I treat the mass 2m to be rotating about mass m and then apply this: Why I am not getting the same answer ?
How to solve this problem in ground frame of reference?
How do we know what is the system rotating about? Is there any other way to solve the problem? I just feel I didn't get it properly.