A child is standing with folded hands at the center 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

Options

A. `K`
B. 2K
C. `(K)/(2)`
D. `(K)/(4)`

Answer

C

Explanation

From the principle of conservation of angular momentum, `l_(1)omega_(1)=l_(2)omega_(2)`
`therefore" "omega_(2)=((l_(1))/(l_(2)))omega_(1)=(omega_(1))/(2)" "(because l_(2)=2l_(1))`
`"Initial KE "(K_(1))=(1)/(2)l_(1)omega_(1)^(2).`
`"New KE"(K_(2))=(1)/(2)l_(2)omega_(2)^(2)`
`therefore" "(K_(2))/(K_(1))=((l_(2))/(l_(1)))(omega_(2)^(2))/(omega_(1)^(2))=(2)/(1)xx(omega_(1)^(2))/(4xxomega_(1)^(2))=(1)/(2)`
`therefore" "K_(2)=(K_(1))/(2)=(K)/(2)`