Q

# Solve! - Properties of Solids and Liquids - JEE Main

If $S$ is  stress and  $Y$ is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

• Option 1)

$2Y/S$

• Option 2)

$S/2Y$

• Option 3)

$2S^{2}Y$

• Option 4)

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

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As we learnt in

Work Done in Stretching Wire / Elastic P.E. -

$=\frac{1}{2}\frac{YAl^{2}}{L}=\frac{1}{2}Fl$

- wherein

L - Length of wire

$l$ - increase in length

$E=\frac{1}{2}\times stress\times strain$

$Y=\frac{stress}{strain}$

$\Rightarrow\ \; Strain = \frac{stress}{Y}$

$E=\frac{1}{2} \times stress\times \frac{stress}{Y}$

$\Rightarrow\ \; E=\frac{1}{2}\frac{s^{2}}{Y}$

Correct option is 4.

Option 1)

$2Y/S$

This is an incorrect option.

Option 2)

$S/2Y$

This is an incorrect option.

Option 3)

$2S^{2}Y$

This is an incorrect option.

Option 4)

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

This is the correct option.

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