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. $\sqrt3/\sqrt2a$
• D. Zero

Answer 1

Answer: (A)

$3v/4a$

Answer 2

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