When is the work done by a force equal to zero

When is the work done by a force equal to zero?

a) If the magnitude of the force is zero, if the magnitude of displacement is zero, or if the angle between the displacement and force vector is 180 degrees.
b) If the magnitude of the force is zero only.
c) If the magnitude of the displacement is zero only.
d) If the magnitude of the force is zero, if the magnitude of displacement is zero, or if the angle between the displacement and force vector is 90 degrees.

d

Letter D is the "most" correct answer because it adequately defines all cases that would result in zero work.

Work is defined as vector force*displacement. (W=F*d)

In any case where the magnitude of the force is zero, no work is done.

In any case where the magnitude of displacement is zero, no work is done.

In any case where the angle between the displacement and force vector is 90 degrees, no work is done because the force and displacement are perpendicular to each other.

a) true except for the angle bit

b) true (but the "only" may make it false, depending on the exact meaning of the word)

c) true (but the "only" may make it false, depending on the exact meaning of the word)

d) true

I'd go with (d) as best choice.