Tension in a string connecting two masses [closed]

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.

1. 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 ?

2. 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.

• I think that solving it in the CM frame gives the system something to pivot about, allowing circular motion and hence making the problem solvable. In the lab frame, B will not remain fixed due to the criteria in the question, making it difficult to analyse. – Physics Jan 5 at 16:48
• In the absence of any further external forces, the linear momentum of the system is constant so the centre of mass travels at a constant velocity $\frac{2v}{3}$ wrt the lab frame. The COM frame is then an inertial frame, so we can apply Newton II to either of the masses. Though since A and B are both accelerating wrt this inertial frame, if we transform into either of them we will need to add some fictitious forces. – James Wirth Jan 5 at 17:32
• You are not satisfied with your solution? It looks like someone else's solution which you are not satisfied with. – sammy gerbil Jan 5 at 22:22
• No. I am not satisfied with _my_solution. That solution isn’t how I solved it. I just linked it because I used to verify my answer. And I clearly described what is that I am not satisfied also. I am trying to solve it in other frames of references. – claws Jan 6 at 4:19
• doubtnut.com/question-answer-physics/… – sammy gerbil Jan 7 at 2:53