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 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: Detailed Explanation:
Young's modulus ($Y$) is an intrinsic property of a material, like density or resistivity.
It is defined as the ratio of stress to strain within the elastic limit:
\[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L / L} \]
While the values of force $F$, area $A$ (related to $r$), and length $L$ can change the resulting deformation, the ratio $Y$ depends solely on the nature of the material (in this case, steel).
Changing the radius or length of the wire does not change the material itself; hence, the Young's modulus remains the same.
Step 3: Final Answer:
The value of $Y$ remains unchanged.