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A negative work is done when an applied force F and the corresponding

June 1, 2025 by rawan239

A negative work is done when an applied force F and the corresponding displacement S are

perpendicular to each other.

parallel to each other.

anti-parallel to each other.

equal in magnitude.

This question was previously asked in

UPSC NDA-2 – 2021

Download PDF Attempt Online

A negative work is done when an applied force F and the corresponding displacement S are anti-parallel to each other.

The work done (W) by a constant force (F) when an object undergoes a displacement (S) is given by the dot product of the force and displacement vectors: $W = \vec{F} \cdot \vec{S} = |\vec{F}| |\vec{S}| \cos\theta$, where $\theta$ is the angle between the force and displacement vectors. Work done is positive when the force and displacement are in the same general direction ($0^\circ \le \theta < 90^\circ$), zero when they are perpendicular ($\theta = 90^\circ$), and negative when they are in opposite directions ($90^\circ < \theta \le 180^\circ$). When the force and displacement are anti-parallel ($\theta = 180^\circ$), $\cos\theta = -1$, and the work done is maximum negative: $W = -FS$.

Examples of negative work include the work done by friction when an object moves (friction acts opposite to motion), or the work done by gravity when an object is lifted upwards (gravity acts downwards while displacement is upwards).

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