The total work done in stretching a wire of cross-sectional area 1 sq. mm and length 200 cm by 0.1 mm, if Young's modulus of the wire is 2 × 10¹¹ N m⁻², is
A
2.5 × 10⁻⁴ J
B
2.5 × 10⁻² J
C
5 × 10⁻² J
D
5 × 10⁻⁴ J
Correct Option:
D
Explanation
Elastic strain energy is W = 1/2 × YA(ΔL)²/L. Here Y = 2 × 10¹¹ N m⁻², A = 1 mm² = 10⁻⁶ m², L = 200 cm = 2 m, and ΔL = 0.1 mm = 10⁻⁴ m. Substitution gives W = 5 × 10⁻⁴ J.
