A uniform rod of volume 2 × 10⁻⁴ m³ is under a uniform tensile stress of 100 MPa. The corresponding longitudinal strain is 5 × 10⁻⁴. Assuming linear elastic behaviour, the total elastic strain energy stored is N J. Find N.
Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity
JEE Mains NEET JEE Advanced

Question

A uniform rod of volume 2 × 10⁻⁴ m³ is under a uniform tensile stress of 100 MPa. The corresponding longitudinal strain is 5 × 10⁻⁴. Assuming linear elastic behaviour, the total elastic strain energy stored is N J. Find N.

Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity

G1 Physics · Accepted Answer

For linear elastic loading, strain-energy density is u = ½σε. Therefore, U = ½σεV. Substitute: σ = 100 MPa = 1×10⁸ Pa, ε = 5×10⁻⁴, V = 2×10⁻⁴ m³. Thus, U = ½ ×1×10⁸ ×5×10⁻⁴ ×2×10⁻⁴. Therefore, U = 5 J. Hence, N = 5.