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

Answer 1

Answer: (B)

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