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dude...when a string is rotating having a mass at its end, we consider the net effect of all the forces to be acceleration towards the center with magnitude v^2/R. So, T = mxa = mv^2/r
Another way to comprehend this is to say , that a centrifugal force away from the center along the radius is working on the mass m. Since the motion of the mass is tangential to the circle, we balance the forces T = Centrifugal force = mv^2/R
Similarly, when the car is moving in a circular track, it is experiencing a centrifugal force of mag. mv^2/R outside OR the net acc. of car is towards the center with mag. of acc. being v^2/R. So, where does the point of frame being inertial or inertial come into picture.
The situation can be interpreted either ways.
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