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Two discs A and B are mounted coaxiallay...

Two discs A and B are mounted coaxiallay on a vertical axle. The discs have moments of inertia I and 2 I respectively about the common axis. Disc A is imparted an initial angular velocity `2 omega` using the entire potential energy of a spring compressed by a distance `x_1` Disc B is imparted an angular velocity `omega` by a spring having the same spring constant and compressed by a distance `x_2` Both the discs rotate in the clockwise direction.
The loss of kinetic energy in the above process is

A

`( I omega^2)/(2)`

B

`(I omega^2)/(3)`

C

`(I omega^2)/(4)`

D

`(I omega^2)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Loss in kinetic energy = (K.E)_(initial)-(K.E.)_(final)`
`=[(1)/(2)I(2omega)^2+(1)/(2)(2I)omega^2]-[(1)/(2)(I+2I)((4)/(3))omega^2]`
`=3I omega^2 -(8)/(3)Iomega^2 = (Iomega^2)/(3)`
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