Question

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$. If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$:

• A. increases by two times
• B. reduces by half
• C. remains unchanged
• D. becomes one fourth

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The topic of this question is the mechanical properties of solids, specifically elasticity.
This question asks how the Young's modulus of a material changes when the physical dimensions (radius and length) of the object made from that material are altered.
Step 2: Key Formula or Approach:
Young's modulus ($Y$) is defined as the ratio of stress to strain within the elastic limit:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L / L} \]
Step 3: Detailed Explanation:
While force $F$, area $A$, and length $L$ determine the deformation, the ratio $Y$ is an intrinsic property of the material.
This means it depends only on the nature of the material (steel) and the ambient temperature.
Modifying the radius or length of the wire does not change the atomic structure of the material itself.
Hence, the value of Young's modulus remains the same regardless of size or shape changes.
Step 4: Final Answer:
The value of $Y$ remains unchanged.