A steel wire of length 20 m is stretched by 2 cm and stores 80 J of elastic potential energy. Find its cross-sectional area in mm². Take Young's modulus Y=2.0×10¹¹ N m⁻².
Physics · Properties of solid and fluid
JEE Mains 2023

Question

A steel wire of length 20 m is stretched by 2 cm and stores 80 J of elastic potential energy. Find its cross-sectional area in mm². Take Young's modulus Y=2.0×10¹¹ N m⁻².

G1 Physics · Accepted Answer

Elastic energy U=(1/2)(YA/L)(ΔL)². Therefore A=2UL/[Y(ΔL)²]. Substituting U=80 J, L=20 m, ΔL=0.02 m and Y=2.0×10¹¹ N m⁻² gives A=40 mm².