Project ForgeStrength of Materials
Stress & Strain
GATE 2017
Expert
A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm², length = 1 m, Young's modulus = 100 GPa) from a height H of 10 mm. If g = 10 m/s², the maximum compression of the elastic bar is __________ mm.
1.51 mm(± 0.01 accepted)
Explanation
Stiffness k = EA/L = (1e11×1e-4)/1 = 1e7 N/m. Energy balance: mg(H+δ) = (1/2)kδ². With mg=1000N: 1000(0.01+δ) = 5e6δ² → 5e6δ²-1000δ-10=0. Solving the quadratic: δ = [1000+√(1000²+4×5e6×10)]/(2×5e6) ≈ 1.518e-3 m ≈ 1.52 mm.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.