A wire suspended vertically from one of its ends is stretched by...

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200N$ to the lower end. The weight stretches the wire by $1$ mm. Then the elastic energy stored in the wire is

Options

A $0. 2J$
B $10J$
C $20J$
D $0. 1J$

Correct answer

D. $0. 1J$

Step-by-step solution

Elastic energy per unit volume =

\dfrac{1}{2} \times \text{stress} \times \text{strain}

∴

Elastic energy =

\dfrac{1}{2} \times \text{stress} \times \text{strain} \times \text{volume}

\dfrac{1}{2} \times \dfrac{F}{A} \times \dfrac{\Delta \text{L}}{L} \times \left(\text{AL}\right)<br /><br />=\dfrac{1}{2}\text{F} \Delta \text{L} = \dfrac{1}{2} \times \text{200} \times {10}^{- 3}\text{=0.1 J}

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