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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), the angular velocity of the platform will vary with the time  as

a)b)c)d)


Question ID - 53226 | Toppr Answer

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), the angular velocity of the platform will vary with the time  as

a)b)c)d)

1 Answer - 5876 Votes

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Answer Key : (c) -

(c)

As there is no external torque, angular momentum will remain constant. When the tortoise moves from  to , figure, moment of inertia of the platform and tortoise decreases. Therefore, angular velocity of the system increases. When the tortoise moves from   to , moment of inertia increases. Therefore, angular velocity decreases

If, =mass of platform

radius of platform

mass of tortoise moving along the chord

perpendicular distance of  from

Initial angular momentum,

At any time , let the tortoise reach  moving with velocity

As 

Angular momentum at time

As angular momentum is conserved

This shows that variation of  with time is nonlinear. Choice (c) is correct



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