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 (w.r.t. the platform), which of the following graphs shows properly the variation of angular velocity of the platform with the time t?
Text Solution
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As there is no external torque, angular momentum will remain constant. When the tortoise moves from A to C, figure, moment of inertia of the platform and tortoise decreases. Therefore, angular velocity of the system increases. When the tortoise moves from C to B, moment of inertia increases. Therefore, angular velocity decreases
If, M=mass of platform
R =radius of platform
m =mass of tortoise moving along the chord AB
a =perpendicular distance of O from AB
Initial angular momentum, 
At any time t, let the tortoise reach D moving with velocity v
As 
Angular momentum at time t.
As angular momentum is conserved
This shows that variation of 
with time is nonlinear. Choice
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