Question

A cubical block of side '$a$' moving on horizontal frictionless surface with velocity '$v$' hits a small nail [coefficient of restitution is e = 0] and rotates about it. Angular velocity of block after hitting the nail is

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

Answer 1

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


Coefficient of restitution (e) = 0.
This means the block gets attached to the nail and rotates about the nail.
The moment of inertia (I) about the corner of a cude and along the edge is $\frac{2}{3}m{a}^2$.
By conservation of angular momentum about nail.
$L_i=L_f$
$mv\frac{a}{2}=\frac{2}{3}m{a}^{2}w$

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