Question

A rod of length $l$ and mass $4m$ is hinged at one end. A point mass $m$ moving with a velocity $v$ hits on the other end and sticks. Find the angular velocity so formed. (Assume the whole system is kept on a smooth horizontal table.)

• A. $\frac{v}{5l}$
• B. $\frac{v}{3l}$
• C. $\frac{2v}{3l}$
• D. $\frac{3v}{7l}$

Answer 1

Answer: (D)

$\frac{3v}{7l}$

Law of conservation of angular momentum
$I\omega =mv\left(l\right)$
$(4\frac{m{l}^2}{3}+m{l}^2)\omega =mvl$
or $\omega =\frac{3v}{7l}$