A bob of mass m , suspended by a string of length l 1 , 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 l 2 , 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 ful

Step-by-step solution

As shown in the figure shown above, the minimum speed required by the bob of mass m attached to the string of length l 1 in order to complete the full circle is 5 g l 1 . When the bob goes to the highest point, its speed becomes g l 1 . Here, it strikes with the identical mass, which is tied to the string of length l 2 . The speed delivered to the object is g l 1 . This should be equal to 5 g l 2 so that this bob could complete a full circle. g l 1 = 5 g l 2 ⇒ g l 1 = 5 g l 2 ⇒ l 1 l 2 = 5