Question

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

• A. decrease continuously
• B. decrease initially and will increase again
• C. remains same
• D. increase continuously

Answer 1

The correct option is B decrease initially and will increase again

As there is no external torque acting on the system, therefore, the angular momentum of the system will remain constant.
$\Rightarrow I\omega =$constant
When non-viscous fluid spreads out, its moment of inertia$\left(m{r}^2\right)$ about the axis of rotation will increase as its distance$\left(r\right)$ from the axis increases. This increases the total moment of inertia$\left(I\right)$ of the system. Thus, angular velocity$\left(\omega \right)$ will decrease.
When the fluid falls from the surface of the platform, the effective mass of the system decreases, therefore, the total moment of inertia$\left(I\right)$ of the system decreases. Thus, angular velocity$\left(\omega \right)$ will increase.
Hence, the angular velocity of the system first decreases and then increases.