What can be the maximum value of the original kinetic energy of disk AA so as not to exceed the maximum allowed value of the thermal energy

The question is incomplete. The complete question is :

In your job as a mechanical engineer you are designing a flywheel and clutch-plate system. Disk A is made of a lighter material than disk B, and the moment of inertia of disk A about the shaft is one-third that of disk B. The moment of inertia of the shaft is negligible. With the clutch disconnected, A is brought up to an angular speed ?0; B is initially at rest. The accelerating torque is then removed from A, and A is coupled to B. (Ignore bearing friction.) The design specifications allow for a maximum of 2300 J of thermal energy to be developed when the connection is made. What can be the maximum value of the original kinetic energy of disk A so as not to exceed the maximum allowed value of the thermal energy?

Solution :

Let M.I. of disk A =

So, M.I. of disk B =  

Angular velocity of A =

So the kinetic energy of the disk A =

After coupling, the angular velocity of both the disks will be equal to ω.

Angular momentum will be conserved.

So,

Now,

Therefore, the maximum initial K.E. = 3066.67 J

double the distance = divide strength by 4