Project ForgeStrength of Materials
Stress & Strain
GATE 2023
Hard
A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with shear modulus 80 GPa. While operating at 500 rpm, the angle of twist across its length is found to be 0.5 degrees. The power transmitted by the shaft at this speed is ______ kW. (Rounded to two decimal places, π=3.14)
238.9 kW(± 3 accepted)
Explanation
θ=0.5×π/180≈0.008722 rad. J=πd⁴/32=3.14×0.1⁴/32≈9.8125×10⁻⁶ m⁴. T=θGJ/L=0.008722×80×10⁹×9.8125×10⁻⁶/1.5≈4564.5 N·m. ω=2πN/60=2×3.14×500/60≈52.33 rad/s. P=Tω≈238.9 kW.
Source: GATE ME 2023 Official Paper (2023)
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.