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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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