A wire of length L and area of cross-section A, is stretched...

A wire of length $L$ and area of cross-section $A$, is stretched by a load. The elongation produced in the wire is $\angle$ If $Y$ is the Young's modulus of the naterial of the wire, then the force constant of the wire is (a) $\frac{Y Z}{A}$ (b) $\frac{Y}{A}$ (c) $\frac{Y A}{L}$ (d) $\frac{Y A}{l}$

A wire of length $L$ and area of cross-section $A$, is stretched by a load. The elongation produced in the wire is $\angle$ If $Y$ is the Young's modulus of the naterial of the wire, then the force constant of the wire is
(a) $\frac{Y Z}{A}$
(b) $\frac{Y}{A}$
(c) $\frac{Y A}{L}$
(d) $\frac{Y A}{l}$

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Key Concepts

Hooke's Law

Hooke's law states that, within the elastic limit of a material, the deformation (strain) of an object is directly proportional to the applied force (stress). This principle is essential for analyzing elastic behavior in materials and is typically expressed through linear relationships between force and displacement, underpinning the concept of the force constant in springs.

Force (Spring) Constant

The force constant, or spring constant, of a material is a measure of its resistance to deformation under applied force. For a uniform wire, it is derived from the relationship between force, extension, Young's modulus, cross-sectional area, and original length. Specifically, by combining Hooke's law with the definition of Young's modulus, the force constant is expressed as k = (Young's modulus × cross-sectional area) / original length.

Young's Modulus

Young's modulus is a measure of the stiffness of a material. It is defined as the ratio of tensile stress (force per unit area) to tensile strain (relative change in length) in the region where Hooke's law applies. This modulus is a fundamental property of a material and quantifies its ability to resist deformation under applied stress.

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