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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 has 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

Asked in NEET 2017 · Conservation of angular momentum

• (1) 1/4I(ω₁-ω₂)²
• (2) I(ω₁-ω₂)²
• (3) 1/8I(ω₁-ω₂)²
• (4) 1/2I(ω₁+ω₂)²

Step-by-step solution

Why the other options are wrong

• (2) comes from dropping the factor 1/4; setting ω₂=0 would then give Iω₁², twice the whole initial energy 1/2Iω₁², which no loss can be
• (3) comes from halving the right answer, as though the combined moment of inertia were 4I rather than 2I
• (4) comes from uses the sum instead of the difference, so it predicts an energy loss even when ω₁=ω₂ and the two discs are already turning together

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