Motion in a vertical circle.

Now Lcos60° + h = L
=> h = L(1 - cos60°)
=> h = L2

I have taken the reference point to be the lowermost point for convenience.

Now if the particle can reach the topmost point, from there it will be able to complete the vertical circle on the action of gravity(correct me if wrong).
Let the topmost point be C.

Energy at B = Energy at critical point C(Tension = 0 at this critical point)

mu₀²2 + mgL2 = 2mgL + 0

=> kmgL + mgL = 4mgL
=> k = 3
So k ≥ 3 for completion of vertical circle.

hey but the answer is given as k≥14/3.