AIPMT PRELIMS 2010 Physics Conservation of Angular Momentum MCQ Question
A circular disk of moment of inertia I₁ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ω₀. Another disk of moment of inertia I_b is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ω_r. The energy lost by the initially rotating disc to friction is
1/2 (I₁I_b / (I₁ + I_b)) ω₀²
1/2 (I_b² / (I₁ + I_b)) ω₀²
I_b / (I₁ + I_b) ω₀²
(I_b - I₁) / (I₁ + I_b) ω₀²
Correct Answer
Detailed Explanation
The energy lost due to friction is the difference between the initial and final kinetic energies. Using the conservation of angular momentum and the given moments of inertia, the energy lost can be calculated as 1/2 (I₁I_b / (I₁ + I_b)) ω₀².
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