Work Power and Energy 4 Question 6

8. 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 massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $l _1 / l _2$ is

(2013 Adv.)

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Answer:

Correct Answer: 8. 5

Solution:

  1. Velocity of first bob at highest point.

$$ v _1=\sqrt{g R}=\sqrt{g l _1} $$

(to just complete the vertical circle)

=velocity of second bob just after elastic collision.

$=$ velocity of second bob at the bottommost point $=\sqrt{5 g l _2}$

$$ \therefore \quad \frac{l _1}{l _2}=5 $$



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