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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.
When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

A

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

B

`(9I omega)/(2t)`

C

`(9I omega)/(4t)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let final velocity be `omega_(1)`, Applying conservation of angular momentum:
`(I + 2I)omega_(1) = I(2omega) + 2 I omega rArr omega_(1) = (4omega)/3`
Now angular impulse = change in angular momentum:
`tau t = 2I (omega_(1)-omega) rArr taut = 2I omega/3 rArr tau = (2I omega)/(3t)`.
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