Two discs of same moment of inertia ( I ) are rotating in same sense about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω 1 and ω 2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss in energy during this process is

Question

Two discs of same moment of inertia ( I ) are rotating in same sense about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω 1 and ω 2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss in energy during this process is, 1 2 I ω 1 + ω 2 2, 1 4 I ω 1 - ω 2 2, I ω 1 - ω 2 2, 1 8 ω 1 - ω 2 2

MARKS App · Accepted Answer

The initial angular momentum of two discs is I 1 ω 1 + I 2 ω 2 = I ω 1 + ω 2 . The final angular momentum of system is I 1 + I 2 ω = 2 I ω From the conservation of angular momentum, ω = ω 1 + ω 2 2 . Initial kinetic energy, K E i = 1 2 I ω 1 2 + ω 2 2 and final kinetic energy, K E f = 1 2 2 I ω 1 + ω 2 2 4 Loss in kinetic energy is Δ K E = 1 2 I 1 I 2 I 1 + I 2 ω 1 - ω 2 2 = 1 2 I 2 2 I ω 1 - ω 2 2 = 1 4 I ω 1 - ω 2 2

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