Question

If a metal rod has length \(\ell\) and area of cross-section \(A\), its Young's modulus is \(Y\). What will happen to \(Y\) if length is doubled and area is halved?

• A. Becomes double
• B. Becomes four times
• C. Becomes halved
• D. Remains same

Answer 1

The Correct Option is D

Concept: Young's modulus: \[ Y=\frac{\text{stress}}{\text{strain}} \] It depends only on the material and not on dimensions such as length or area. Thus even if \[ \ell \rightarrow 2\ell, \qquad A \rightarrow \frac{A}{2} \] Young's modulus remains unchanged. \[ \boxed{Y=\text{constant}} \]