Two discs A & B having small projections, welded on their circumference , are free to rotate about their fixed axes, which are parallel to each other as shown in figure. The disc B starts rotating with angular velocity ω . It’s projection hits the projection of other disc at rest after time T. The coefficient of restitution is 12 . The two discs are of same radius but their moments of inertia are 4I and I respectively.The angular velocity of the disc A after collision isThe second collision between projections will take place after a minimum time of

Let B rotates in clockwise direction initiallyJust after collision, let ω1,ω2 are their angular speeds and J is the impulse of collision. For discs⁡(1&2),JR=4Iω1=Iω+ω2⇒4ω1=ω+ω2 …….(1)e=12⇒12=Rω1−Rω2Rω⇒ω=2ω1−2ω2    .......(2)From (1) and (2),  ω1=310ω,ω2=ω5 i.e., disc (2) reverses its direction of rotationLet left and right discs make N1, N2 number of rotations between first and 2nd collision between projections. N1T1=N2T2N12π(3ω/10)=N22πω/5⇒N1=32N2 Least integer values of N1 and N2 are N1=3,N2=2∴ Time of second collision t0=N1T1=3⋅2π3ω(10)=20T[∵T=π/ω]Let B rotates in clockwise direction initiallyJust after collision, let ω1,ω2 are their angular speeds and J is the impulse of collision. For discs⁡(1&2),JR=4Iω1=Iω+ω2⇒4ω1=ω+ω2 …….(1)e=12⇒12=Rω1−Rω2Rω⇒ω=2ω1−2ω2    .......(2)From (1) and (2),  ω1=310ω,ω2=ω5 i.e., disc (2) reverses its direction of rotationLet left and right discs make N1, N2 number of rotations between first and 2nd collision between projections. N1T1=N2T2N12π(3ω/10)=N22πω/5⇒N1=32N2 Least integer values of N1 and N2 are N1=3,N2=2∴ Time of second collision t0=N1T1=3⋅2π3ω(10)=20T[∵T=π/ω]