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Two coaxial discs, having moments of ine...

Two coaxial discs, having moments of inertia `l_(1) and (I_(1))/(2)` are rotating with respective angular velocities `omega and (omega_(1))/(2)` about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If `E_(f) and E_(i)` are the final and initial total energies, then `(E_(f)-E_(i))` is:

A

`-(I_(1)omega_(l)^(2))/(24)`

B

`-(I_(1)omega_(l)^(2))/(12)`

C

`(I_(1)omega_(1)^(2))/(6)`

D

`(3)/(8)I_(1)omega_(1)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(L_(1))=vec(L_(f))`
`I_(1)omega_(1)+(I_(1))/(2)(omega_(1))/(2)=I_(1)omega_(f)+(I_(1))/(2)omega_(f)`
`(5I_(1)omega_(1))/(4)=(3)/(2)I_(1)omega_(f)impliesomega_(f)=(5)/(6)omega_(1)`
`Delta K.E =((1)/(2)I_(1)omega_(f)^(2)+(1)/(2)(I_(1))/(2)omega_(f)^(2))-((1)/(2)I_(1)omega_(1)^(2)+(1)/(2)(I_(1))/(2)((omega_(1))/(2))^(2))`
= `(1)/(2)*(3)/(2)I_(1)(25)/(36)omega_(1)^(2)-(1)/(2)*(9)/(8)I_(1)omega_(1)^(2)`
= `(75I_(1)omega_(1)^(2))/(144)-(9)/(16)I_(1)omega_(1)^(2)`
= `(75-81)/(144)I_(1)omega_(1)^(2)`
`DeltaK.E = -(1)/(24)I_(1)omega_(1)^(2)`
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