A child is standing with folded hands at the centre of the platform rotating about its central axis. The rotational kinetic energy of the system is ' K '. The child now stretches his arms so

Question

A child is standing with folded hands at the centre of the platform rotating about its central axis. The rotational kinetic energy of the system is ' K '. The child now stretches his arms so that the moment of inertia of the system doubles. The rotational kinetic energy of the system now is ' K 1 ​ '. The ratio K 1 ​ / K is

TestHub · Accepted Answer

By the principle of conservation of angular momentum, the angular momentum $L$ of the system remains constant since no external torque acts on it.

The rotational kinetic energy $K$ is given by $K = \frac{L ^{2}}{2 I}$ , where $I$ is the moment of inertia.

When the child stretches his arms, the new moment of inertia becomes $I_{1} = 2 I$ .

The new rotational kinetic energy $K_{1}$ is $K_{1} = \frac{L ^{2}}{2 I _{1}} = \frac{L ^{2}}{2 ( 2 I )} = \frac{1}{2} (\frac{L ^{2}}{2 I}) = \frac{K}{2}$ .

Therefore, the ratio $\frac{K _{1}}{K} = \frac{1}{2}$ .

Answer: $\frac{1}{2}$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion