A child is standing with folded hands at the centre of a platform rotating about its central axis. ….

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 doubles. The kinetic energy of the system now is

(a) 2K

(b) K/2

(c) K/4

(d) 4K

Ans: (b)

Sol: From Conservation of Angular momentum

I ω = constant

I₁ ω₁ = I₂ ω₂

I₁ ω₁ = 2 I₁ ω₂

ω₂ = ω₁/2

$\large K = \frac{L^2}{2I_1}$

$\large K’ = \frac{L^2}{2 I_2}$

$\large K’ = \frac{L^2}{2 (2 I_1)} = \frac{K}{2}$