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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

`(2Iomega)/(3t)`

B

`(9Iomega)/(2t)`

C

`(9Iomega)/(4t)`

D

`(3Iomega)/(2t)`

Text Solution

Verified by Experts

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