First slide

Elastic Modulie

Question

A metal rod (Young's modulus Y) has a length I and of cross-section A. The work done in stretching the rod by an amount $∆$ L is

Easy

A

$\frac{YA (ΔL)^{2}}{2 L}$
B

$\frac{YA (ΔL)^{2}}{L}$
C

$\frac{YA (ΔL)}{2 L}$
D

$\frac{YA (ΔL)}{L}$

Solution

We know that
Energy/volume= $= \frac{1}{2} \times stress \times strain$
Further, Y $= stress / strainorstress = Y \times strain$
$∴ Energy = \frac{1}{2} (Y \times strain) \times strain \times volume$
$\begin{array}{l} = \frac{1}{2} Y (strain)^{2} \times volume \\ = \frac{1}{2} Y (ΔL / L)^{2} AL \\ = \frac{1}{2} YA (ΔL)^{2} / L \end{array}$

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