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

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) (K/2) (C) (K/4) (D) 4K

Tardigrade Admin · Accepted Answer

According to the principle of conservation of angular momentum,

I ω

= constant
As

I

is doubled, w becomes half.
Now K.E. of rotation,

K = \frac{1}{2} I ω^{2}

Since

I

is doubled and

ω

is halved, therefore
K.E. will become half

i . e \frac{K}{2}

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

$2 K$

$\frac{K}{2}$

$\frac{K}{4}$

$4 K$

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

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

2K

2K​

4K​

4K