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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}

 
Answers (1)
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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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