The relationship between force and position is shown in Fig....

The relationship between force and position is shown in Fig. $4.19$ (in one-dimensional case). The work done by the force in displacing a body from $x=1 \mathrm{~cm}$ to $x=$ $5 \mathrm{~cm}$ is
(A) 20 ergs
(B) $60 \mathrm{ergs}$
(C) 70 ergs
(D) 700 ergs

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Key Concepts

Units of Work and Energy

Work is measured in units of energy. In different systems of measurement, these units vary. For example, the SI unit is the joule, while in the centimeter-gram-second (CGS) system, the unit is the erg. Understanding these units helps in accurately comparing the work calculated under different measurement systems.

Graphical Interpretation of Work

In a force versus displacement graph, the work done is represented by the area under the force curve between the initial and final positions. This visual method helps in understanding how changes in force with position contribute to the overall work done.

Integration of Force Over Displacement

When a force varies with position, the work done cannot be obtained simply by multiplying the force by the displacement. Instead, it is calculated by integrating the force function over the path of the displacement. This integral calculates the sum of all infinitesimal contributions of work along the path.

Work in Physics

Work is the measure of energy transfer when a force acts upon an object to cause displacement. In physics, it is defined as the product of the component of the force in the direction of displacement and the magnitude of the displacement, indicating how much energy is expended or transferred.

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