If the radius of wire stretched by a load is doubled, then its Young’s Modulus will be

Explanation:

Young's Modulus:

• Young's Modulus, denoted as E, is a measure of the stiffness of a material. It is a mechanical property that quantifies the ratio of tensile stress to tensile strain in the linear elastic region of a material. Mathematically, it is expressed as:

E = Stress / Strain

Where:

• Stress = Force (F) / Cross-sectional Area (A)
• Strain = Change in Length (ΔL) / Original Length (L)

Key Concept: Young's Modulus is an intrinsic property of a material, meaning it depends only on the material's nature and not on its shape, size, or dimensions (such as radius, length, or cross-sectional area). It describes the material's ability to resist deformation under tensile stress.

If the radius of a wire stretched by a load is doubled, its Young's Modulus remains unaffected. This is because Young's Modulus is an inherent property of the material and does not depend on the geometric dimensions of the object. While changing the radius alters the cross-sectional area of the wire, which in turn affects the stress and strain values individually, the ratio of stress to strain (Young's Modulus) remains constant for a given material.

Let’s break this down:

1. Stress: Stress is calculated as Force (F) divided by Cross-sectional Area (A). If the radius of the wire is doubled, the cross-sectional area increases by a factor of four (since A = πr², and r is doubled). Consequently, stress decreases by a factor of four.
2. Strain: Strain is the ratio of the change in length (ΔL) to the original length (L). The change in length is influenced by the applied force and the material's properties, but strain remains proportional to stress for elastic deformations (Hooke's Law).
3. Young's Modulus: Since Young's Modulus is the ratio of stress to strain, and both stress and strain scale proportionally with the change in cross-sectional area, their ratio (E) remains unchanged.