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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 | SaraNextGen Top 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
127 votes
Answer Key / Explanation : (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

127 votes


127