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To calculate the moment of inertia at o, I tried to apply (1/3mq^2) but I am not sure if it is correct. Any help would be appreciated.
It looks like the question assumes the rod to be of negligible mass.
Then the rotational moment of inertia is just $I=mq^2 $
You may have confused the moment of inertia of a rod of mass m with length q.
Required, but never shown