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JEE Main · 2011 · 10 Apr 2011 · Offline · Rotational Mechanics

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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc:
  1. (A)continuously decreases
  2. (B)continuously increases
  3. (C)first increases and then decreases✓ Correct
  4. (D)remains unchanged

Answer: (C)

Solution

There is no external torque on the disc-and-insect system about the axis, so the angular momentum is conserved. As the insect walks inward from the rim towards the centre its distance from the axis falls, the moment of inertia decreases, and to keep fixed the angular speed must rise. Once it passes the centre and moves out towards the far rim its distance grows again, increases and falls back. So across the whole journey the angular speed first increases and then decreases.

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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