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:
- 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 $=\sqrt{5 g l _2}$
$$ \therefore \quad \frac{l _1}{l _2}=5 $$
