Question

A dancer is standing on a rotating platform taking two sphere on her hands . If she drops down the sphere on ground then dancer's

• A. angular velocity will increase
• B. angular momentum and angular velocity both will unchanged
• C. angular momentum unchanged and angular velocity will increase
• D. both will decrease

Answer 1

The correct option is C angular momentum unchanged and angular velocity will increase

When the dancer puts down the spheres, the mass of the system changes and hence the angular velocity of the system changes.

We know that;

$L=I\omega$

Where,

$L$=Angular Momentum

$I$= Moment of inertia of the rotating object. and

$\omega$=angular velocity.

Also,

$I=m{r}^2$

Also, if there is no external torque is acting on the system, the angular momentum of the system will remain conserve.

Thus, when the dancer drops the ball, the mass of the system will decrease. For conserving the momentum, consequently, the angular velocity of the system will increase.

Hence, option c is correct.