Question

A non-zero force is acting on a body but work done is zero. Which of the following statement(s) justify the above situation?

• A. Displacement is zero.
• B. Force is perpendicular to the direction of displacement.
• C. Force is parallel to displacement.
• D. Force is opposite to the direction of displacement.

Answer 1

Answer: (A), (B)

The correct options are
A

Displacement is zero.

B

Force is perpendicular to the direction of displacement.

The mathematical expression for work done is
$Workdone=F\times S\times cos\left(\theta \right)$
where
$S$ is displacement,
$F$ is the magnitude of force,
$\theta$ is the angle between force and direction of displacement.
Since force is non-zero, there are only two variables in the equation that can make the work done zero i.e., displacement $\left(S\right)$ and $cos\left(\theta \right)$.
Case I: $cos\left(\theta \right)$ is zero when $\theta$ is 90° i.e., force is perpendicular to the displacement.
Case II: displacement $S$ is zero.