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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω₁ and ω₂. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:

1. (a) 1/4 (ω₁ − ω₂)²
2. (b) I(ω₁ − ω₂)²
3. (c) 1/8 (ω₁ − ω₂)²
4. (d) 1/2 (ω₁ − ω₂)²

Correct answer: (c) 1/8 (ω₁ − ω₂)²

Solution

When the two discs come into contact, they will eventually rotate with a common angular velocity due to conservation of angular momentum. The loss of energy is given by the difference between the initial and final rotational kinetic energies. Using the formula for rotational kinetic energy and solving, the loss of energy is found to be (1/8)I(ω₁ − ω₂)².

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