Question

A student plotted a graph from his readings on the determination of Young's modulus of a metal wire but forgotten to label. The quantities on x and y cannot represent :

• A. weight hung and extension
• B. stress applied and extension
• C. stress applied and strain produced
• D. stress applied and energy stored

Answer 1

The correct option is D stress applied and energy stored

$U=\frac{1}{2}\left(stress\right)\left(strain\right)$

$=\frac{1}{2}\left(\frac{F}{A}\right)\left(\frac{\Delta L}{L}\right)$

$=\frac{1}{2}\left(\frac{F}{A}\right)\left(\frac{F}{Ay}\right)$

$=\frac{1}{2y}(stress{)}^2$

The graph of option (D) would be parabolic as: $U\propto (stress{)}^2.$