Question

A child is standing with folded hands at the
centre of a platform rotating about its central
axis. The K.E of the system is K. The child
now stretches his arms so that the M.I of the
system doubles. The K.E of the system now
is

1) 2K

(2) K/2

3) 4K

4) K/4​

Answer 1

Answer:

Explanation:

According to the principle of conservation of angular momentum, Iω = constant

As I is doubled, ω becomes half.

Now K.E. of rotation,

K.E = 1/2Iw^2

Since I is doubled and ω is halved, K.E. will become half i.e., K/2

Hope it works !!

Answer 2

Answer:

2

Use angular momentum conservation

$I \omega = constant \\ I\omega = 2I \omega' \\ \omega' = \frac{ \omega}{2}$

So energy previously was

$k = \frac{1}{2} I{ \omega}^{2}$

Now

$k '= \frac{1}{2} \times 2 I \times ({ \omega \over2})^{2} = \frac{1}{2} ( \frac{1}{2} I { \omega}^{2} ) = \frac{k}{2}$