AAPT hard problem help

I can’t wrap my head around this problem?
I think that when you drill a whole like that, the cylinder will roll back to attain its equilibrium so need to hold it with a certain torque to keep it in place, but i do not know how to find the torque

What i have in mind is:
since T=dL/dt, but L=Iw(w is angular velocity) so T=Ia(a is angular acceleration). So i’m trying to find a balanced torque but i do not know how to find the new moment of inertia? Do we use the parallel axis theorem? or it doesn’t work because there’s hole in it?? HELP!!


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