A thin rod of length 1 m and area of cross-section 3 × 10⁻⁶ m² is suspended vertically from one end. The rod is cooled from 210°C to 160°C. After cooling, a mass M is attached at the lower end such that the length again becomes 1 m. Young's modulus and coefficient of linear expansion are 2 × 10¹¹ N m⁻² and 2 × 10⁻⁵ K⁻¹ respectively. The value of M is ____ kg. [g = 10 m s⁻²]
Physics · Circular Motion
JEE Mains 31 January 2023 Shift 1 Morning Shift

Question

A thin rod of length 1 m and area of cross-section 3 × 10⁻⁶ m² is suspended vertically from one end. The rod is cooled from 210°C to 160°C. After cooling, a mass M is attached at the lower end such that the length again becomes 1 m. Young's modulus and coefficient of linear expansion are 2 × 10¹¹ N m⁻² and 2 × 10⁻⁵ K⁻¹ respectively. The value of M is ____ kg. [g = 10 m s⁻²]

Physics · Circular Motion

JEE Mains 31 January 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Thermal contraction ΔL = LαΔT = 1×2×10⁻⁵×50 = 10⁻³ m. The required tensile strain is 10⁻³. Stress = Y×strain = 2×10¹¹×10⁻³ = 2×10⁸ N m⁻². Force = stress×area = 2×10⁸×3×10⁻⁶ = 600 N, so M = 600/10 = 60 kg.