Question

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its center. At some instant of time a viscous fluid of mass $m$ is dropped at the center and is allowed to spread out and finally fall. The angular velocity during this period

• A. decreases continuously
• B. decreases initially and increases again
• C. remains unaltered
• D. increases continuously

Answer 1

Answer: (B)

From law of conservation of angular momentum if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is $J=I\omega =$ constant Hence, if $I$ decreases, $\omega$ increases and viceversa. When liquid is dropped, mass increases hence $I$ increases $\left(I=m{r}^2\right)$. So, $\omega$ decreases, but as soon as the liquid starts falling $\omega$ increases again.