Question

A rod $AB$ of length $L$ and mass $M$ is free to move on a frictionless horizontal surface. It is moving with a velocity $v$, as shown in figure. End $B$ of rod $AB$ strikes the end of the wall. Assuming elastic impact, the angular velocity of the rod $AB$, just after impact, is

• A. $\frac{v}{2 L}$
• B. $\frac{3 v}{L}$
• C. $\frac{3 v}{2 L}$
• D. $\frac{v}{L}$

Answer 1

Answer: (B)

From the conservation of angular momentum,
$\Rightarrow M v_{c m} \frac{L}{2}+\frac{M L^{2}}{12} \omega=\frac{M v L}{2} \Rightarrow v_{c m}+\frac{\omega L}{6}=v$
From the conservation of linear momentum,
$\Rightarrow \frac{\omega L}{2}-v_{c m}=v \Rightarrow \omega\left(\frac{L}{2}+\frac{L}{6}\right)=2 v$
$\therefore \omega=\frac{3 v}{L}$