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 . 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  will vary with time  as a)b)c)d)

(b)

Since there is no external torque, angular momentum will remain conserved. The moment of inertia will first decrease till the tortoise moves from  to  and then increase as it moves from  to . Therefore  will initially increase and then decrease

Let  be the radius of platform  the mass of tortoise and  is the mass of platform

Moment of inertia when the tortoise is at

and moment of inertia when the tortoise is at

Here

From conservation of angular momentum

Substituting the values we can found that the variation of  is non linear