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

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Q: 29 (NDA-I/2022)
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

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,11,45,23,18,4,11

keywords: 

{'pulley': [0, 0, 1, 2], 'displacement': [0, 1, 0, 3], 'horizontal plane': [0, 0, 0, 3], 'force anti': [0, 0, 0, 1], 'work': [1, 1, 10, 7]}

The correct answer is option 4, negative. When a force is applied in a direction opposite to the displacement of an object, the work done on the object is considered negative.

To understand why, we need to recall the formula for work done: work = force × displacement × cos(angle between force and displacement). In this case, the force and displacement are anti-parallel, which means they are in opposite directions. As a result, the angle between them is 180 degrees, and cos(180) = -1.

Therefore, when the force is applied anti-parallel to the displacement, the work done is given by the formula work = force × displacement × -1. Since the angle is 180 degrees, cos(180) = -1, and the work done has a negative value.

This negative work done indicates that energy is being taken away from the object. In the case of dragging a mass on a horizontal plane, the force is acting against the motion, causing a decrease in the object`s kinetic energy. Hence, the work done is negative.