Work Energy And Power Question 279
Question: Two small bodies of masses ’m’ and ‘2m’ are placed in a fixed smooth horizontal circular hollow tube of mean radius ‘r’ as shown. The mass ’m’ is moving with speed ‘u’ and the mass ‘2m’ is stationary. After their first collision, the time elapsed for next collision is [ coefficient of restitution e = 1/2 ]
Options:
A) $ \frac{2\pi r}{u} $
B) $ \frac{4\pi r}{u} $
C) $ \frac{3\pi r}{u} $
D) $ \frac{12\pi r}{u} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] If just after collision, relative velocity = v then
$ \frac{v}{u}=\frac{1}{2}\therefore {\omega _{rel}}=\frac{v}{r}=\frac{u}{2r} $
$ \therefore $ time between 1st and 2nd collision, $ t=\frac{2\pi }{{\omega _{rel}}} $
$ =\frac{4\pi r}{u} $
