1.

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

Answer»

`-(I_(1)omega_(1)^(2))/(24)`
`-(I_(1)omega_(1)^(2))/(12)`
`3/8 I_(1)omega_(1)^(2)`
`1/6 I_(1)omega_(1)^(2)`

Solution :From conservation of Angular momentum about the axis:
Li = LF
`rArr I_(1)omega_(1) + I_(1) /2 XX omega_(1)/2 =(I_(1) + I_(1)/2) omega_(f) rArr omega_(f)=(5/4 I_(1)omega_(1))/(3/2 I_(1)) = 5/6 omega_(1)`
`therefore E_(f) - E_(i) = 1/2 (I_(1) + I_(1)/2) omega_(f)^(2) -[1/2 I_(1)omega_(1)^(2) +1/2(I_(1)/2)(omega_(1)/2)^(2)] =1/2 xx (3I_(1))/2 (5/6 omega_(1))^(2) -9/16 I_(1)omega_(1)^(2) = (I_(1)omega_(1)^(2))/24`


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