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A mass M is dragged by a pulley on a horizontal plane by a force anti-

June 1, 2025 by rawan239

A mass M is dragged by a pulley on a horizontal plane by a force anti-parallel to its displacement. The work done in pulling the mass M is

zero

positive

infinite

negative

This question was previously asked in

UPSC NDA-1 – 2022

Download PDF Attempt Online

Work done (W) is calculated as the dot product of force (F) and displacement (d): W = F ⋅ d = |F| |d| cos(θ), where θ is the angle between the force vector and the displacement vector. The problem states that the force is “anti-parallel” to its displacement. This means the force and displacement vectors are in opposite directions, so the angle between them is 180 degrees. The cosine of 180 degrees (cos(180°)) is -1. Therefore, the work done is W = |F| |d| (-1) = -|F| |d|. Since the magnitude of force and displacement are positive, the work done is negative.

Work done is negative when the force and displacement are in opposite directions (anti-parallel).

Work done is positive when the force and displacement are in the same direction (parallel, θ=0°, cos(0°)=1). Work done is zero when the force is perpendicular to the displacement (θ=90°, cos(90°)=0).

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