Question

A metal wire of length L, area of cross-section A and Young modulus Y behaves as a spring of spring constant

• 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 $K=\frac{YA}{L}$

$Y=\frac{F}{A}\frac{l}{\Delta l}$

$F=\frac{YA}{L}\text{. Sl}$

$\begin{array}{c}\text{Where}\Delta l\text{is increcye in length}\\ \text{for spring}\\ F=kx.\end{array}$

$\begin{array}{c}\text{Where}x\text{is same as}\Delta l\\ \text{equating}\left(1\right)\text{and}\left(2\right)\\ K=\frac{YA}{L}\end{array}$