A child stands, hands at the side, on a turntable. The kinetic energy of system is K. The child now raises his arms, and the moment of inertia of system becomes twice. Then the kinetic energy of system will be …………

Options

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

Answer

B

Explanation

No external force is acting so angular momentum is constant
`therefore I_(1)omega_(1)=I_(2)omega_(2)`
`therefore omega_(2)=(I_(1)omega_(1))/(I_(2))=(omega_(1))/(2)[because I_(2)=2I_(1)]`
Now rotational kinetic energy
`therefore K_(1)=(1)/(2)I_(1)omega_(1)^(2)` and
`therefore K_(2)=(1)/(2)I_(2)omega_(2)^(2)`
`=(1)/(2)(2I_(1))((omega_(1))/(2))^(2)`
`=(1)/(2)(I_(1)omega_(1)^(2))/(2)`
`=(K)/(2)`