Let a mass m is tied to a string of length l and is rotated in a vertical circle with centre at the other end of the string.

            Total force towards centre = 

            For the movement in the circle, the string should have tight i.e. the tension has to be positive at all positions.

            As the tension is low at the top T_top ≥0

                      mv_t²/l -mg  ≥ 0          

Now,    let v_b be the velocity at the bottom. As the particle goes up, its KE decreases and GPE (Gravitational Potential Energy) increases

        Loss in KE = gain in GPE              

Now, if the same particle of mass m is loosening from a string of length  fixed to the point O, and let v be the needed velocity imparted to the particle.

The particle just stops at a instance B, then

Loss in KE = Gain in GPE

1/2mv² - 0 = mgl       

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