In the formula \(W=Fs\cos\theta\), the angle between force and displacement (\(\theta\)) is equal to 90°, the net work done will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Zero
Work done by a force is \(W=Fs\cos\theta\), where \(\theta\) is the angle between the force and the displacement. Only the part of the force along the displacement does work.
\(\theta=90^\circ\), so \(\cos90^\circ=0\)
\(W=Fs\times0=0\)
A force at right angles to the motion does no work; for example, the force of gravity on a bag carried along a level road, or the pull of the string on a stone whirled in a circle.
Why the other options are incorrect
Option (1) Double — Incorrect. \(\cos\theta\) is never more than 1, so the work can never exceed \(Fs\), let alone double it.
Option (2) Positive but not double — Incorrect. Work is positive only for angles less than 90°, where \(\cos\theta\) is positive.
Option (3) Negative — Incorrect. Work is negative only for angles more than 90°, as with friction opposing motion.