A thin uniform rod of mass ‘M’ and length ‘L' rotating about a perpendicular axis passing through its center with a constant angular velocity ' $ω$ '.Two objects each of mass $\frac{M}{3}$ are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of :

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$\frac{1}{3} ω$

$\frac{1}{7} ω$

$\frac{1}{2} ω$

$\frac{1}{6} ω$

answer is D.

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Detailed Solution

According To Law of Conservation of Angular Momentum.

$\begin{array}{l} L_{i} = L_{f} \\ \frac{M L^{2}}{12} \times ω = [\frac{M L^{2}}{12} + 2 \frac{M}{3} {(\frac{L}{2})}^{2}] ω_{f} \\ \frac{ω}{3} = ω_{f} \end{array}$

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