Two discs, each having moment of inertia 5 kg m² about its central axis, rotating with speeds 10 rad s^-1 and 20 rad s^-1 are brought in contact face to face with their axes
of rotation coincided. The loss of kinetic energy in the process is

When brought in contact , due to kinetic friction , both acquire common velocities.

Applying conservation of angular momentum,

$\begin{array}{l}(5+5)\omega \text{'}=5\times 10+5\times 20=150\\ \Rightarrow \omega \text{'}=15{\mathrm{rads}}^{-1}\end{array}$

Initial kinetic energy

$\begin{array}{l}=\frac{1}{2}\times 5\times 10\times 10+\frac{1}{2}\times 5\times 20\times 20\\ =250+1000=1250\mathrm{J}\end{array}$

Final kinetic energy $=\frac{1}{2}\times 10\times 15\times 15=1125\mathrm{J}$

Loss of kinetic energy $=(1250-1125)\mathrm{J}=125\mathrm{J}$