Subtopic: Measurement of force, stress, torque, speed, displacement and acceleration on machine elements – shafts, couplings, keys, bearings and knuckle joints
Question Statement:
The root mean square acceleration for mechanical vibration of a tractor is 3.15 m s⁻² and its frequency is 80 Hz. The root mean square amplitude of the vibration in μm is ___________. [round off to two decimal places] (Take π = 3.14)
Official Answer Key:
12.20 to 12.80
Step-by-Step Solution & Explanation
• a_rms = ω²x_rms, ω=2πf=502.4 rad/s, ω²=252405.76
• x_rms = 3.15/252405.76 = 1.248×10⁻⁵ m = 12.48 μm
Computed value: x_rms ≈ 12.48 μm (within official range 12.20–12.80)
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.