Two discs each having moment of inertia $5 k g$ $m^{2}$ about its central axis, rotating with speeds $10 r a d s^{- 1}$ and $10 r a d$ $s^{- 1}$ , are brought in contact face to face with their axes of rotation coincided. The loss of kinetic energy in the process is:

2 J

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5 J

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125 J

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0 J

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Solution

The correct option is C $0 J$
Let $w^{'}$ be the final angular velocity,
$L_{i} = L_{f}$
$I w_{i} + I w_{i} = (2 I) w^{'} ⟹ w^{'} = w = 10 r a d / s$
Initial K.E, $E_{i} = 2 \times \frac{1}{2} I w^{2} = I w^{2}$
Final K.E, $E_{f} = \frac{1}{2} (2 I) (w^{'})^{2} = I w^{2}$
Thus $Δ E = 0 J$

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