A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can rotate freely about a fixed vertical axis through its midpoint O. Two rings each of mass 1 kg initially at rest are placed at a distance of 10 cm from O on either side of the rod. The rod is set in rotation with an angular velocity of 30 radian per sec and when the rings reach the ends of the rod, the angular velocity in rad/s is

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answer is B.

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Detailed Solution

According to the conservation of angular momentum $I_{1} ω_{1} = I_{2} ω_{2}$
$∴ [\frac{M L^{2}}{12} + 2 m r^{2}] ω_{1} = [\frac{M L^{2}}{12} + 2 m {(\frac{L}{2})}^{2}] ω_{2}$
or $[\frac{0.75 \times {(0.4)}^{2}}{12} + 2 \times 1 \times {(0.1)}^{2}] \times 30$
$[\frac{0.75 \times {(0.4)}^{2}}{12} + 2 \times 1 \times {(0.2)}^{2}] \times ω^{2}$
or $ω_{2} = \frac{(0.01 + 0.02) 30}{(0.01 + 0.08)} = \frac{0.03 \times 30}{0.09} = 10 r a d / s$

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