A pendulum bob hung from a string of length L is released from height h above the bottom of its swing. The pendulum’s swing is interrupted by a horizontal peg at height r above the bottom of the pendulum’s swing (point B). After the string hits the peg, the bob swings around in a circular arc of radius r. Express your answers in terms of L, r, and g, as needed. 

(a) If the bob is to travel in a full circle of radius r around the peg without the string going slack, what is the minimum possible speed it can have at the top of that circle (point A)? 

(b) If the string breaks when the bob is at point A, moving at the minimum speed found in part (a), how far to the right of point B is the bob when it’s at the same height as point B? 

(c) What is the minimum value of h for which the bob will make it to point A without going slack?

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B