Question

A uniform rod of mass $m$ and length $L$ can rotate freely on a smooth horizontal plane about a vertical axis hinged at point $O$. A point mass having same mass $m$ coming with an initial speed $u$ perpendicular to the rod, strikes the rod in-elastically at its free end. Find out the angular velocity of the rod just after collision?

• A. $\omega =\frac{4u}{3L}$
• B. $\omega =\frac{3u}{4L}$
• C. $\omega =\frac{5u}{4L}$
• D. $\omega =\frac{4u}{5L}$

Answer 1

The correct option is B $\omega =\frac{3u}{4L}$

Angular momentum is conserved about $O$ because no external torque is acting about it.

$\Rightarrow L_i=L_f$

$\Rightarrow muL+0=(\frac{m{L}^2}{3}+m{L}^2)\omega$

$\Rightarrow \omega =\frac{3u}{4L}$