Question

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. $2K$
• B. $\frac{K}{2}$
• C. $\frac{K}{4}$
• D. $4K$

Answer 1

Answer: (B)

$\frac{K}{2}$

Answer 2

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 $i.e \frac{K}{2}$