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

The relationship between force and position is shown in figure given (in one dimensional case). The work done by the force is displaying a body from $x=1 \mathrm{~cm}$ to $x=5 \mathrm{~cm}$ is
(a) $20 \mathrm{erg}$
(b) $60 \mathrm{erg}$
(c) 70 erg
(d) $700 \mathrm{erg}$

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Key Concepts

Work

Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force. It is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. In general, if the force is variable, the work done is computed as the integral of the force with respect to displacement.

Integration in Physics

Integration is a mathematical tool used in physics to calculate quantities that accumulate continuously. When computing work done by a variable force, the process involves performing a definite integral of the force function over the specified interval of displacement. This technique generalizes the concept of work beyond situations where the force is constant.

Graphical Interpretation of Work

The work done by a force can be determined from the area under a force versus displacement graph. When the force varies with position, the area under the curve between the initial and final positions represents the total work done by the force. This graphical method provides a visual way to understand and calculate work in physics.

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