Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2. They are brought into contactface to face coinciding the axis of rotation. The expression for loss of energy during this process is[NEET 2017]

When no external torque acts on system, then angularmomentum of system remains constant.Angular momentum before contact=Iω1+I2ω2=Iω1+Iω2=Iω1+ω2Angular momentum after the discs brought into contact=Inet ω=I1+I2ω=2IωFrom law of conservation of angular momentum,Iω1+ω2=2Iω⇒ω=ω1+ω22Now, to calculate loss of energy, we subfract initial and final energies of system.Loss of energy=12Iω12+12Iω22−12(2I)ω2=14Iω1−ω22