Question bank/JEE Main/Physics

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 $\omega(t)$ will vary with time t as

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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 and D.
The re fore $\omega$ will initially increase and then decrease. Let R be
the radius of platform m the mass of disc and M is the mass of platform.
Moment of inertia when the tortoise is at A
and moment of inertia when the tortoise is at B
$I_{2} = {mr}^{2} + \frac{{MR}^{2}}{2}$
here $r^{2} = a^{2} + {\lbrack\sqrt{R^{2} - a^{2}} - vt\rbrack}^{2}$
From conservation of angular momentum
$\omega_{0}I_{1} = \omega(t)I_{2}$
substituting the values we can see that variation of $\omega(t)$ is
nonlinear.

Source: Grass-G / P-07 Physics paper 17 October.docx