Question

A metal wire of length $L$, area of cross-section $A$ and Young’s modulus $Y$ behaves as a spring of spring constant $K$. Which of the following is correct?

• A. $K=\frac{YA}{L}$
• B. $K=\frac{2YA}{L}$
• C. $K=\frac{YA}{2L}$
• D. $K=\frac{YL}{A}$

Answer 1

The correct option is A $K=\frac{YA}{L}$

Let the force $F$ produces an extension $x$ in the wire of length $L$
$\mathrm{St}ress=\frac{F}{A},Strain=\frac{x}{L}Y=\frac{F/A}{x/L}=\frac{FL}{xA}$
Equivalent spring constant, $K=\frac{F}{x}=\frac{YA}{L}$