A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy of the system is ' $\mathrm{K}$ '. The child now stretches his arms so that the moment of inertia of the system becomes double. The kinetic energy of system now is

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Aicharya · Accepted Answer

$\begin{aligned} \mathrm{K} & =\frac{1}{2} \mathrm{I} \omega^2 \ \mathrm{I}^{\prime} & =2 \mathrm{I} \end{aligned}$ By law of conservation of angular momentum $\begin{aligned} & \mathrm{I}^{\prime} \omega^{\prime}=\mathrm{I} \omega \ & 	herefore 2 \mathrm{I} \omega^{\prime}=\mathrm{I} \omega \ & 	herefore \omega^{\prime}=\frac{\omega}{2} \ & \mathrm{~K}^{\prime}=\frac{1}{2} \mathrm{I}^{\prime} \omega^{\prime 2}=\frac{1}{2}(2 \mathrm{I})\left(\frac{\omega}{2}ight)^2=\frac{1}{2}\left(\frac{1}{2} \mathrm{I} \omega^2ight)=\frac{\mathrm{K}}{2} \end{aligned}$ .

A child is standing with folded hands at the centre of the platform rotating about its central axis. The…

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