Question

A small uniform rod AB of mass M and length l rotates freely with angular velocity ${\omega }_0$ in a horizontal plane about a vertical axis passing through one of its end A. A small sleeve of mass M starts sliding along the rod from A. Angular velocity of rod when sleeve reaches the other end, is

• A. $\frac{{\omega }_0}{4}$
• B. $\frac{2{\omega }_0}{3}$
• C. $\frac{13{\omega }_0}{15}$
• D. $\frac{{\omega }_0}{3}$

Answer 1

The correct option is A $\frac{{\omega }_0}{4}$

C.O.A.M
$\frac{M{I}^2}{3}{\omega }_0=(\frac{M{I}^2}{3}+M{I}^2)\omega$
$\omega =\frac{{\omega }_0}{4}$