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 doubles. The kinetic energy of the system now is

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

Answer 1

Answer: (B)

$\frac{K}{2}$

In the absence of external torque, $Iw=constant$

Thus $\frac{w_1}{w_2}=\frac{I_2}{I_1}$

Rotational K.E, $K=\frac{1}{2}I{w}^2$

$\frac{K^{\prime }}{K}=\frac{I_2{w}_2^2}{I_1{w}_1^2}=\frac{I_1}{I_2}$

Given : $I_2=2I_1⟹K^{\prime }=\frac{K}{2}$