Question

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ${\omega }_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega \left(t\right)$ will vary with time $t$ as

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The angular momentum $\left(L\right)$ of the system is conserved; i.e., $L=I\omega =\text{costant}.$
When the tortoise walks along a chord, it first moves closer to the centre and then away from the centre. Hence, $I$ first decreases and then increases. As a result, $\omega$ will first increase and then decrease. Also, the change in $\omega$ will be a nonliner function of time.
Hence, $\left(B\right)$ is the correct answer.