A thin elastic circular ring of radius 1 m is made from a material of density 8000 kg/m³ and Young's modulus 2 × 10¹¹ Pa. It rotates in its own plane with angular speed 50 rad/s. If its circumferential strain is N × 10⁻⁴, find N.
Physics · Properties of solid and fluid · properties of solid stress ,strain and modulus of elasticity
JEE Mains NEET JEE Advanced

Question

A thin elastic circular ring of radius 1 m is made from a material of density 8000 kg/m³ and Young's modulus 2 × 10¹¹ Pa. It rotates in its own plane with angular speed 50 rad/s. If its circumferential strain is N × 10⁻⁴, find N.

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

G1 Physics · Accepted Answer

For a rotating elastic ring, strain = [ρω²R²] / Y. Substitute: ρ = 8000, ω = 50, R = 1, Y = 2×10¹¹. Therefore, strain = [8000×50²] / [2×10¹¹] = 1×10⁻⁴. Hence, N = 1.