Two discs `A` and `B` are mounted coaxially ona vertical axle. The discs have moments of inertia `l` and `2l` respectively about the common axis. Disc A is imparted an initial angular velocity `2 omega` using the centre potential energy of a spring compressed by a distance `x_(1)`. Disc `B` is imparted angular velocity `omega` by a spring having the same spring constant and compressed by a distance `x_(2)`. Both the disc rotate in the clockwise direction.
When disc `B` is brought in contact with disc `A`, they acquirea common angularvelocity in time `t`. The average frictional torque on one disc by the other during this period is -

Options

A. `(2I omega)/(3 t)`
B. `(9 I omega)/(3 t)`
C. `(9 I omega)/(4 t)`
D. `(9 I omega)/(2 t)`

Answer

A

Explanation

Let `omega'` be the common velocity. Applying conservation of angular momentum.
`(I + 2I) omega' = I. 2 omega + 2I .omega`
or `omega' = (I(2omega) + 2I(omega))/(3 I) = (4 omega)/(3)`….(i)
Now, `omega' = omega + (tau)/(2 I) t` ….(ii)
From Eqs. (i) and (ii), `tau = (2 I omega)/(3 t)`.