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  4. A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is

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Q. A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is

JIPMERJIPMER 2014System of Particles and Rotational Motion

Solution:

According to the principle of conservation of angular momentum,
$I \omega $ = constant
As $I$ is doubled, w becomes half.
Now K.E. of rotation, $K = \frac{1}{2} I \omega^2$
Since $I$ is doubled and $\omega$ is halved, therefore
K.E. will become half $i.e \frac{K}{2}$