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 platform. Now the platform is given an angular velocity $ω_{0} .$ When the tortoise moves along the chord of the platform with a constant velocity (with respect to the platform); The angular velocity of platform $ω (t)$ will vary with time $‘ t ’$ as

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answer is B.

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Detailed Solution

Since there is no external torque, angular momentum remains conserved.

As moment of inertia initially decreases and then increases, the $ω$ will increase initially and then decrease.

Moment of inertial when tortoise is at B

$I = {mr}^{2} + \frac{{MR}^{2}}{2};$ where $r^{2} = a^{2} + {[\sqrt{R^{2} - a^{2}} - vt]}^{2}$

M=mass of tortoise; M=mass of disc.

Therefore, the variation of $ω$ is non-linear.

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