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 given by

• 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

$ Y=\frac{F/A}{\Delta l/l} $ $ \Rightarrow $ $ F=YA\frac{\Delta l}{l} $ ...(i) If $ k $ is spring constant, $ F=k\Delta l $ ... (ii) Comparing Eqs. (i) and (ii), we get $ k=\frac{YA}{l} $