A wire of length L and cross-sectional area A is made of a...

A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y .$ If the wire is stretched by an amount $x$, the work done is
(A) $\frac{Y A x^{2}}{2 L}$
(B) $\frac{Y A x}{2 L^{2}}$
(C) $\frac{Y A x}{2 L}$
(D) $\frac{Y A x^{2}}{L}$

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Key Concepts

Elastic Potential Energy

The energy stored in a material when it is deformed elastically is known as elastic potential energy. For a material obeying Hooke's law, this energy is given by one half the product of the force and the displacement (or equivalently, one half the spring constant times the square of the displacement), making it a key concept in understanding work done during elastic deformation.

Young's Modulus

A measure of a material's stiffness, defined as the ratio of stress (force per unit area) to strain (relative deformation). It characterizes how much a material will stretch or compress under a given load, laying the groundwork for understanding elastic behavior in materials.

Hooke's Law

This principle states that, within the elastic limit of a material, the force required to extend or compress the material is directly proportional to the displacement or change in length. It provides a linear relationship between force and extension, which is essential for calculating the elastic force in stretching problems.

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