Question

The rotational inertia of a disk about its axis is
0.70 kg .m². When a 2.0 kg weight is added to
its rim, 0.40m from the axis, the rotational
inertia becomes:​

Answer 1

Assuming the new mass is distributed evenly around the periphery at that distance of 0.4 m, then you are just adding 2 kg x (0.4m)^2 to the existing moment of inertia. 0.7+0.32 = 1.02 kg-m^2.