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Question:

A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is :

Solution:

The initial speed of 1st bob (suspended by a string of length l1) is √5gl1. The speed of this bob at the highest point will be √gl1. When this bob collides with the other bob their speeds will be interchanged. √gl1 = √5gl2 → l1/l2 = 5