Question

A thin rod of mass M and length l stands along z-axis. Its lower end is hinged at the center of a disc of same mass M and radius R. The disc is on XY plane with its center at the origin. The whole arrangement is rotating freely about z-axis with an angular velocity ${\omega }_0$. If the rod falls on disc and rotates with the disc. The angular speed of the arrangement is

• A. $\frac{{\omega }_0{R}^2}{l^2+R^2}$
• B. $\frac{3{\omega }_0{R}^2}{2l^2+3R^2}$
• C. $\frac{6{\omega }_0{R}^2}{l^2+6R^2}$
• D. $\frac{6{\omega }_{0}R}{l+6R}$

Answer 1

The correct option is B $\frac{3{\omega }_0{R}^2}{2l^2+3R^2}$

Conservation of angular momentum
$L_i-L_f\Rightarrow {\omega }_0\times \frac{m{R}^2}{2}=\omega [\frac{m{R}^2}{2}+\frac{m{l}^2}{3}]\Rightarrow {\omega }^{\prime }=\frac{3{\omega }_0{R}^2}{3R^2+2l^2}$