Rotational MotionHard

Question

Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its center of mass and perpendicular to the rod then angular velocity of the system about A is :

Options

A.$\frac{3}{2}\frac{\text{ }L}{{md}^{2}}$
B.$\frac{2\text{ }L}{{md}^{2}}$
C.$\frac{4}{3}\frac{\text{ }L}{{md}^{2}}$
D.$\frac{2\text{ }L}{5{md}^{2}}$

Solution

$L = I\omega$ and $\omega = \frac{L}{I}$

$${\omega = \frac{L}{m\left( \frac{2\text{ }d}{3} \right)^{2} + 2\text{ }m\left( \frac{\text{ }d}{3} \right)^{2}} = \frac{L}{\frac{4}{9}{md}^{2} + \frac{2}{9}{md}^{2}} = \frac{L}{\frac{6{md}^{2}}{9}} }{\omega = \frac{3\text{ }L}{2{md}^{2}}}$$

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