An ice skater spins at `3pi" rad s"^(-1)` with hers arms extended. If her moment of inertia with arms folded is `75%` of that with arms extended, her angular velocity when she fold her arms is

Options

A. `(pi)"rad s"^(-1)`
B. `(2pi)"rad s"^(-1)`
C. `(3pi)"rad s"^(-1)`
D. `(4pi)"rad s"^(-1)`

Answer

D

Explanation

Here, `omega_(1)="3 pi rad s"^(-1), l_(1)=l`
`l_(2)=(75)/(100)l_(1)=(3)/(4)l, omega_(2)=?`
`"As "l_(2)omega_(2)=l_(1)omega_(1)`
`therefore" "omega_(2)=(l_(1))/(l_(2))xx omega_(1)=(4)/(3)3pi = 4pi " rad s"^(-1)`