Question

Young’s modulus of a material is \( Y \). If the length of a wire is doubled and the cross-sectional area is halved, then Young’s modulus will be:

• A. \( Y/4 \)
• B. \( 4Y \)
• C. \( Y \)
• D. \( 2Y \)

Hint:

Young’s modulus remains unchanged when only geometric factors like length and area are modified.

Answer 1

The Correct Option is C

Step 1: {Young's modulus dependency} 
\[ Y = \frac{{Stress}}{{Strain}} \] Step 2: {Effect of change in length and area} 
Young's modulus is a material property and does not depend on length or cross-sectional area. Thus, the correct answer is \( Y \). 
 

Answer 2

Step 1: Young’s modulus \( Y \) is a property of the material, not dependent on the shape or size of the specimen.
It is defined as:
\( Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L} = \frac{F L}{A \Delta L} \)

Step 2: In this formula:
- \( F \) = force applied
- \( A \) = cross-sectional area
- \( L \) = original length
- \( \Delta L \) = elongation

Step 3: If the length is doubled and the area is halved, the values of \( L \) and \( A \) change, but Young's modulus remains the same because:
- It is an intrinsic property of the material.
- It depends only on the nature of the material and not on dimensions like length or area.

Final Answer: The Young’s modulus remains \( Y \)