The tension in the string is same in both cases because of the similar mass or weight of the bodies.
Both pulleys have the same mass and same diameter, but one is solid and the other is a hoop, then there is same tension occurs in both cases because tension depends on mass which is similar on both side. We know that tension is the opposite force of the weight.
So we can conclude that the tension in the string is same in both cases because of the similar mass or weight of the bodies.
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