Question

When the force is perpendicular to the ___________, no work is said to be done.

Answer 1

As a very first step, one could recall the definition for work done. You may recall that the work done could be defined as the dot product of force and displacement. You could simply check for the condition when the angle between them is $90{}^\circ$and hence find the answer.

Formulas used:
Work done,
$W=F\bullet S=FS\cos \theta$

Complete step-by-step solution:
In the question, we are asked to find the condition when no work is said to be done. We are given that when force is perpendicular to a certain physical parameter then no work is said to be done and we are supposed to find this physical parameter.
Let us recall the definition for work done. Work is defined as the product of magnitude of the displacement and the force component along that direction. In other words, we could say that work done is the dot product of force and displacement. Mathematically, we could express this as,
$W=F\bullet S=FS\cos \theta$
Here, $\theta$is known to be the angle between force and displacement. When this angle is equal to $90{}^\circ$, that is, when force and displacement are perpendicular to each other, work done would become zero. That is,
$W=FS\cos 90{}^\circ =0$
So, clearly, we could conclude that when force and displacement are perpendicular to each other, the work done would be zero.

Note: Another common definition for work done is the amount of energy being transferred. Since work done is the dot product of displacement and force, another possibility for work done to be zero is when either of these quantities is zero. Work done can also be positive as well as negative.