(Solution) - A pendulum consisting of a bob of mass M on -(2025 Original AI-Free Solution)

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A pendulum, consisting of a bob of mass M on a cord of length L, is interrupted in its swing by a peg a distance d below its point of suspension.

(a) If the bob is to travel in a full circle of radius (L ? d) around the peg, what is the minimum possible speed it can have at the lowest point in its motion, just before it starts to go around? Ignore any decrease in the length of the string due to the peg's circumference.
(b) From what minimum angle ( must the pendulum be released so that the bob attains the speed calculated in (a)?