Energy stored per unit volume in a stretched wire having Young's modulus Y and stress ' S ' is

Question

Energy stored per unit volume in a stretched wire having Young's modulus Y and stress ' S ' is (A) ( text YS /2) (B) (S2 Y/2) (C) (S2/2 Y) (D) (S/2 Y)

Tardigrade Admin · Accepted Answer

Δ U =(1/2) × stress × strain =(1/2) × text stress × ( text stress /Y) ∵ text Stress =Y text . strain =(1/2) × (S2/Y)

Q. Energy stored per unit volume in a stretched wire having Young's modulus $Y$ and stress ' $S$ ' is

$\frac{YS}{2}$

$\frac{S ^{2} Y}{2}$

$\frac{S ^{2}}{2 Y}$

$\frac{S}{2 Y}$

$Δ U = \frac{1}{2} \times$ stress $\times$ strain
$= \frac{1}{2} \times stress \times \frac{stress}{Y}$
${∵ Stress = Y . strain}$
$= \frac{1}{2} \times \frac{S ^{2}}{Y}$

Q. Energy stored per unit volume in a stretched wire having Young's modulus Y and stress ' S ' is

2 YS ​

2S2Y​

2YS2​

2YS​