A wire suspended vertically from one of its ends is...

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{~N}$ to the lower end. The weight stretches the wire by $1 \mathrm{~mm}$. The elastic energy stored in the wire is (A) $0.2 \mathrm{~J}$ (B) $10 \mathrm{~J}$ (C) $20 \mathrm{~J}$ (D) $0.1 \mathrm{~J}$

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200 \mathrm{~N}$ to the lower end. The weight stretches the wire by $1 \mathrm{~mm}$. The elastic energy stored in the wire is
(A) $0.2 \mathrm{~J}$
(B) $10 \mathrm{~J}$
(C) $20 \mathrm{~J}$
(D) $0.1 \mathrm{~J}$

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Key Concepts

Hooke's Law

Hooke's Law states that, within the elastic limit of a material, the force required to extend or compress the material is directly proportional to the displacement. This proportional relationship is mathematically expressed as F = kx, where F is the force applied, x is the displacement or extension, and k is the spring constant.

Spring Constant

The spring constant is a measure of the stiffness of an elastic material or spring. It is defined by the ratio of the applied force to the resulting displacement (k = F/x). A higher spring constant indicates a stiffer material, which requires more force to achieve the same displacement.

Elastic Potential Energy

Elastic potential energy is the energy stored in an elastic material as a result of its deformation under the action of a force. This energy can be calculated using the formula E = 1/2 k x^2, where k is the spring constant and x is the displacement. It represents the work done in stretching or compressing the material and is released when the material returns to its original dimensions.

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