A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is \(600 \times 10^{-6} \mathrm{~m}^{3}\). The elastic potential energy stored in the wire in stretched condition would be ______ J. (Given Young modulus of copper \(=1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\))

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Elasticity & SHM

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is

600 \times 1 0^{- 6} m^{3}

. The elastic potential energy stored in the wire in stretched condition would be ______ J. (Given Young modulus of copper

= 1.1 \times 1 0^{11} N / m^{2}

)

Answer: 33

The elastic energy stored per unit volume of a stretched wire is

\frac{1}{2} \times stress \times strain = \frac{1}{2} Y (strain)^{2}

. The longitudinal strain here is

\frac{Δ L}{L} = \frac{3 \times 1 0 ^{- 3}}{3} = 1 0^{- 3}

. The total energy is this density multiplied by the volume,

U = \frac{1}{2} Y (strain)^{2} V = \frac{1}{2} (1.1 \times 1 0^{11}) (1 0^{- 3})^{2} (600 \times 1 0^{- 6})

. Evaluating,

U = \frac{1}{2} (1.1 \times 1 0^{11}) (1 0^{- 6}) (6 \times 1 0^{- 4}) = 33 J

. The elastic potential energy stored in the stretched wire is

33 J

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Integer answer