Question

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

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

Answer 1

Answer: (A)

$r^2=\frac{a^2}{2}$
Net torque about $O$ is zero.
Therefore, angular momentum $(L)$ about $O$ will be conserved, or $L_i=L_f$
$Mv\left(\frac{a}{2}\right)=I_0\omega =\left(I_{cm}+M{r}^2\right)\omega$
$=\left\{\left(\frac{M{a}^2}{6}\right)+M\left(\frac{a^2}{2}\right)\right\}\omega$
$=\frac{2}{3}M{a}^2\omega$
$\omega =\frac{3v}{4a}$