Answer
(d) A nonzero net external force acts on the object in Case B only.
Work Step by Step
Newton's 2nd law states that $$\sum F=ma$$
This means an object is under the influence of a nonzero net external force only if it has some acceleration $a$ to it.
In Case A, since the object is traveling at a constant speed, which means it has no acceleration and thus cannot have a nonzero net external force acted on.
In Case B, the object is traveling with acceleration $a=9.8m/s^2$, which means it has a nonzero net external force acted on.
