Rotation 2 Question 9

9. 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 ω0. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform ω(t) will vary with time t as

(2002)

(a)

(c)

(b)

(d)

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Answer:

Correct Answer: 9. (c)

Solution:

  1. 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. Therefore, ω 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

I1=mR2+MR22

and moment of inertia when the tortoise is at B

I2=mr2+MR22 Here, r2=a2+[R2a2vt]2

From conservation of angular momentum

ω0I1=ω(t)I2

Substituting the values, we can see that variation of ω(t) is non-linear.



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