Q56 / 60 · JEE Advanced 2013 (Paper 1) · Physics

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 l1l2 is

Correct answer: 5

Solution

Figure
As shown in the figure shown above, the minimum speed required by the bob of mass m attached to the string of length l1 in order to complete the full circle is 5gl1.
Figure
When the bob goes to the highest point, its speed becomes gl1. Here, it strikes with the identical mass, which is tied to the string of length l2. The speed delivered to the object is gl1. This should be equal to 5gl2 so that this bob could complete a full circle.   
gl1=5gl2
⇒gl1=5gl2
⇒l1l2=5

Hence, the correct answer is 5.

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