A dancer is standing on a stool rotating about the vertical axis passing through its centre. She pulls her arms towards the body reducing her moment of inertia by a factor of n. The new angular speed of turn table is proportional to

Options

A. `n`
B. `n^(-1)`
C. `n^(0)`
D. `n^(2)`

Answer

A

Explanation

Since, no external torque is acting the angular momentum (L) is conserved.
`L=l omega="constant"`
`therefore" "L=l_(1)omega_(1)=l_(2)omega_(2)`
`because" "l_(2)=(l)/(n)`
`therefore" "(l)/(n) omega_(2)=l omega rArr omega_(2)=nomega`