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Any idea? @gleem
For starters lets determine what condition must be satisfied in order to solve the problem. When the string hits the peg the ball will rotate around the peg but the velocity of the ball must be sufficient to keep it rotating at least to the top of its motion directly above the peg. For that to happen the net force on the ball at this point must be zero i.e., no net downward force. Can you write this condition considering the weight of the ball and the centripetal force.
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