Explanation

(b) Since there is no external torque, angular momentum will remain conserved. The moment of inertia will first decrease till the tortoise moves from $A$ to $C$ and then increase as it moves from $C$ to $D$. Therefore $\omega$ will initially increase and then decrease
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Let $R$ be the radius of platform $m$ the mass of tortoise and $M$ is the mass of platform
Moment of inertia when the tortoise is at $A$
$I_{1} = mR^{2} + \frac{MR^{2}}{2}$
and moment of inertia when the tortoise is at $B$
$I_{2} = mr^{2} + \frac{MR^{2}}{2}$
Here $r^{2} = a^{2} + \left\lbrack \sqrt{R^{2} - a^{2}} - vt \right\rbrack^{2}$
From conservation of angular momentum $\omega_{0}I_{1} = \omega_{(t)}I_{2}$
Substituting the values we can found that the variation of $\omega_{(t)}$ is non linear