Question

# A wire of length $$L$$ and cross-sectional A is made of a material of Young's modulus. If the wire is stretched  by an amount x, the work done is....................

Solution

## Work done is equal to the potential energy stored in the wire.$$\therefore$$       $$W = U = \dfrac{1}{2} \times Stress \times Strain \times Volume$$OR         $$W = \dfrac{1}{2} \times Y (Strain)^2 \times Volume$$                    .............(1)               $$(Strain = Y \times Strain)$$   $$Strain = \dfrac{x}{L}$$            and    Volume$$=AL$$$$\therefore$$    $$W = \dfrac{1}{2} \times Y \times \dfrac{x^2}{L^2} \times AL$$                $$\implies W = \dfrac{Y x^2 A}{2L}$$Physics

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