Question

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

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

Answer 1

The correct option is A $\frac{3v}{4a}$

Iitial angular momentum $L_i=mv\frac{a}{2}$
fianl angular momentum $L_f=I\times \omega$

By momentum conservation,
$L_i=L_{f}mv\frac{a}{2}=I\times \omega$
$\omega =\frac{mva}{2I}$ ....(1)
where $I_{cube}=\frac{2m{a}^2}{3}$
on putting eq. (1)

$\omega =\frac{3v}{4a}$