Q82 / 180 · AIIMS 2014 · Physics

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

  • A
    $2 K$
  • Correct answer
    B
    $\frac{K}{2}$
  • C
    $\frac{K}{4}$
  • D
    $4 K$

Solution

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

Hence, the correct answer is option: 'B'.

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