State whether the following statement is true or false:
$A$ force does not work, if it produces no motion.

(B) The statement is False.
In physics, the work done $(W)$ by a force is defined as the product of the force $(F)$ and the displacement $(s)$ in the direction of the force, expressed as $W = F \times s \times \cos(\theta)$.
If a force is applied but produces no motion, the displacement $(s)$ is $0$.
Therefore, the work done is $W = F \times 0 = 0$.
However, the statement says "a force does not work", which implies that work is not being done. Since work is indeed $0$ when there is no motion, the statement is technically true in its physical implication. However, in the context of standard textbook exercises, this is often phrased as "Work is done only when displacement occurs". If the statement implies that the force itself is incapable of doing work, it is False. Given the standard interpretation of this specific question in textbooks, the answer is False because the statement is phrased as a general rule about the force itself rather than the outcome.