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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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
(a) When disc B is brought in contact with disc 4
Let `omega'` be the final angular velocity of both the disc rotating together. Apply conservation of angular momentum for the two disc system.
`I(2omega) + 2(omega) = (I+2I)omega' rArr omega' = (4)/(3) omega`
Torque on disc A
`tau_A = (DeltaL_A)/(t) = (L_f -L_i)/(t) = (Ixx(4)/(3)omega-Ixx2omega)/(t) = (-2Iomega)/(3t)`
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