question_answer

A bar of mass \['m'\] length \[\ell \] is pure translator motion with its centre velocity \[v\]. It collides with another identical bar which is in rest and sticks to it. Assume that after the collision it becomes one system, then the angular velocity of the system after the collision is

A) \[\frac{1}{5}\frac{v}{\ell }\]                 

B) \[\frac{2}{5}\frac{v}{\ell }\]

C) \[\frac{3}{5}\frac{v}{\ell }\]                 

D) \[\frac{v}{\ell }\]

Correct Answer: C

Solution :

[c] Conservation of angular momentum of combined system about centre of mass of the system \[mg\frac{\ell }{4}={{I}_{com}}\omega =\frac{10}{24}m{{\ell }^{2}}\omega \] \[\Rightarrow \omega =\frac{3}{5}\frac{v}{\ell }\]