question_answer

Two points of a rod move with velocities 3\[v\] and perpendicular to the rod and in the same direction, separated by a distance 'r'. Then the angular velocity of the rod is

A) \[\frac{3v}{r}\]            

B) \[\frac{4v}{r}\]

C) \[\frac{5v}{r}\]            

D) \[\frac{2v}{r}\]

Correct Answer: D

Solution :

[d]  \[{{\omega }_{rad}}={{\omega }_{po\operatorname{int}}}=\left( \frac{{{v}_{rel}}}{r} \right);{{v}_{rel.}}\] being the velocity of one point w.r.t. other. \[=\frac{3v-v}{r}\]and 'r' being the distance between them. \[=\frac{2v}{r}\]