Question

In the limit that the moment of inertia I→0 while the mass m remains finite, what magnitudes would you expect for the tension T in the vertical section of string and the downward acceleration a of the center of mass?

Answer 1

Here are the possible answers:
T=0 and a=0
T=0 and a=g
T=mg and a=0
T=∞ and a=g
T=0 and a=∞
T=mg and a=g