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A child is standing with his two arms folded at the centre of a turntable that is rotating about its central axis with an angular speed $ω_{0}$ . Now, the child outstretches his hands so that moment of inertia of the system becomes three times the initial value .The new angular speed is

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$\frac{ω_{0}}{3}$

$\frac{ω_{0}}{6}$

$ω_{0}$

$6 ω_{0}$

answer is B.

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Detailed Solution

Here,
Initial angular speed, $ω_{i} = ω_{o}$
Initial moment of inertia = $I_{i}$
Final moment of inertia $I_{f} = 3 I_{i}$
According to the law of conservation of angular momentum, we get

$L_{i} = L_{f}$

$I_{1} ω = I_{f} ω_{f}$

$ω_{f} = \frac{I_{i} ω_{i}}{I_{f}} = (\frac{I_{i}}{I_{f}}) ω_{i} = (\frac{I_{i}}{3 I_{i}}) ω_{i} (∵ I_{f} = 3 I_{i})$

= $\frac{ω_{i}}{3} = \frac{ω_{0}}{3} (∵ ω_{i} = ω_{0})$

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