Two uniform circular disc plates A and B are mounted co-axially 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 $2 ω$ . Disc $B$ is imparted an angular velocity $ω$ . 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

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$\frac{3 I ω}{2 t}$

$\frac{9 I ω}{2 t}$

$\frac{2 I ω}{3 t}$

answer is A.

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Detailed Solution

If $τ$ is the average frictional torque and the relative motion occurs for time $t$ , then $τ t$ is the angular impulse imparted to each disc but in the opposite sense
Now, we can write that $τ . t = I (ω^{1} - 2 ω)$ or $τ . t = 2 I (ω^{1} - ω)$
Each of the above equation gives $τ = 2 I ω / 3 t$