A small body attached to a light string of length R is projected from the lowest point of a vertical circle. The minimum speed at the bottom required to complete the circle is:
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A small body attached to a light string of length R is projected from the lowest point of a vertical circle. The minimum speed at the bottom required to complete the circle is:

G1 Physics · Accepted Answer

For the limiting case at the top, tension is zero, so v_top²=gR. By energy conservation from bottom to top: ½mv_bottom² = ½mgR + 2mgR = (5/2)mgR. Hence v_bottom=√(5gR).