Questions

# 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 ${\omega }_{1}$ and ${\omega }_{2}$. They are brought into contactface to face coinciding the axis of rotation. The expression for loss of energy during this process is[NEET 2017]

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a
12Iω1+ω22
b
14Iω1−ω22
c
Iω1−ω22
d
I8ω1−ω22

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detailed solution

Correct option is B

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