In which of the following situations will an applied force do negative work on a body?
[amp_mcq option1=”The applied force and displacement of the body are at 135° to each other” option2=”The applied force and displacement of the body are parallel to each other” option3=”The applied force and displacement of the body are perpendicular to each other” option4=”The applied force and displacement of the body are at 45° to each other” correct=”option1″]
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UPSC Geoscientist – 2023
Work is negative when $\cos \theta$ is negative. This occurs when the angle $\theta$ is between 90° and 270° (exclusive of 90° and 270° where work is zero).
Let’s examine the options:
A) Angle is 135°. $\cos 135° = -1/\sqrt{2}$. Since $\cos \theta$ is negative, the work done is negative.
B) Angle is 0° (same direction) or 180° (opposite direction). If $\theta=0°$, $\cos 0° = 1$, work is positive. If $\theta=180°$, $\cos 180° = -1$, work is negative. So, parallel force and displacement *can* result in negative work (if opposite directions), but doesn’t *always*.
C) Angle is 90°. $\cos 90° = 0$. Work is zero.
D) Angle is 45°. $\cos 45° = 1/\sqrt{2}$. Since $\cos \theta$ is positive, work is positive.
Option A is the only situation listed that guarantees the work done by the applied force is negative.