A small ball is attached to an end of a light string of length R. It is suspended in vertical plane supported at point A. B and C are two nails (of negligible thickness) at a horizontal distance 0.3 R from A and a vertical distance 0.4 R above A respectively. The ball is given a horizontal velocity `u = sqrt5gR)` at its lowest point. Subsequently, after the string hitting the nails, the nails become the centre of rotation. Assume no loss in kinetic energy when the string hits the nails. It is known that the string will break if tension in it is suddenly increased by 200% or more.

Will the string break during the motion? If yes, where? What is tension in the string at the instant the string breaks?

Answer

The string will break on hitting the second nail at C.T = 8.6 mg