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Two coaxial discs, having moments of ine...

Two coaxial discs, having moments of inertie `I_1` and `I_1/2` are rotating with respective angular volecities `omega_1` and `(omega1)/2`, about their common axis.They are brought in contact with each other and thereafter they rotate with a common angular volecity.If `E_f` and `E_i` are the final and initial total energies, then `(E_f-E_1)` is:

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
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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