A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is 2.0 × 10¹¹ N m⁻². The longitudinal strain produced in the wire is ______ × 10⁻⁵.
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 1 Morning Shift

Question

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is 2.0 × 10¹¹ N m⁻². The longitudinal strain produced in the wire is ______ × 10⁻⁵.

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Longitudinal strain is strain = stress/Y Stress: σ = F/A Radius r = 20 mm = 0.020 m Area: A = πr² = π(0.020)² Force: F = 62.8 kN = 6.28×10⁴ N Thus, σ = 6.28×10⁴ / [π(0.020)²] = 5.0×10⁷ N m⁻² Therefore, strain = (5.0×10⁷)/(2.0×10¹¹) = 2.5×10⁻⁴ = 25×10⁻⁵ Final value: 25