A thin solid disc of mass 1 kg and radius 25 cm is rotating about its own geometrical axis AB with angular velocity 12 rad/s. A particle of mass 1 kg is gently attached to the rim of the disc. Then new angular velocity of the disc is

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A thin solid disc of mass 1 kg and radius 25 cm is rotating about its own geometrical axis AB with angular velocity 12 rad/s. A particle of mass 1 kg is gently attached to the rim of the disc. Then new angular velocity of the disc is

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$6 rad/s$

$4 rad/s$

$3 rad/s$

$8 r a d / s$

answer is B.

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Detailed Solution

Conserving angular momentum,

$(I_{1} + I_{2}) ω = I_{1} . ω_{0}$

$\Rightarrow ω = \frac{ω_{0}}{(1 + \frac{I_{2}}{I_{1}})} = \frac{R}{(1 + \frac{1 \times 25^{2}}{\frac{1}{2} \times 1 \times 25^{2}})} \frac{r a d}{s} = 4 \frac{r a d}{s}$