Question

A cubical block of side $a$ is moving with velocity $v$ on a horizontal smooth plane as shown in figure. It hits a ridge at point $O$. The angular speed of the block after it hits $O$ is

• A. $3 v /(4 a)$
• B. $3 v /(2 a)$
• C. $\sqrt{3 v} / \sqrt{2 a}$
• D. zero

Answer 1

Answer: (A)

Apply conservation of angular momentum about $O$
$M v \frac{a}{2}=\left[\frac{M a^{2}}{6}+M\left(\frac{a}{\sqrt{2}}\right)^{2}\right] \omega$
$\Rightarrow \omega=\frac{3 v}{4 a}$