Question

A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular velocity of $20rad/s$. When the stretches her arms fully, the spinning speed decreases in $10rad/s$/. If $I$ is the initial moment of inertia of the dancer, the new moment of inertia is

• A. $21$
• B. $31$
• C. $I/2$
• D. $I/3$

Answer 1

The correct option is A $21$

Here, angular momentum is conserved.

Initial angular momentum = Final angular momentum

$I\times 20=I^{\prime }\times 10$

where, $I^{\prime }$ is the new moment of inertia.

Then,

$I^{\prime }=2I$