Q. A rod of length $l$ is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is
A) $\sqrt{3gl}$
B) $\sqrt{2gl}$
C) $2\ Ml^{2}$
D) None of these
Explanation
(a) As the mass is concentrated at the centre of the rod, therefore,
$mg \times \frac{l}{2} = \frac{1}{2}I\omega^{2} = \frac{1}{2}\left( \frac{ml^{2}}{3} \right)\omega^{2}$
or $l^{2}\omega^{2} = 3gl$
[image:7_image104.emf]
Velocity of other end of the rod
$v = l\omega = \sqrt{3gl}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.