The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is I…

The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is I. It is rotating with angular velocity ω. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is
  1. Iω22
  2. Iω24
  3. Iω26
  4. Iω28

Solution

From conservation of angular momentum

I 1 ω 1 = I 2 ω 2

Iω=2I ω 2

ω 2 = ω 2

New KE=12.(2I)(ω2)2=Iω24

Loss in  KE=12Iω2Iω24=Iω24
 

Asked in: JEE Mains - Rotational Motion - Test 3

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