GATE 2021 ME (ME2) – Question 64
The torque provided by an engine is given by $T=12000+2500\sin(2\theta)$ N.m, where $\theta$ is the angle turned by the crank from inner dead center. The mean speed of the engine is 200 rpm and it drives a machine that provides a constant resisting torque. If variation of the speed from the mean speed is not to exceed ±0.5%, the minimum mass moment of inertia of the flywheel should be _____ kg.m² (round off to the nearest integer).
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Correct answer: 570
Explanation
The constant resisting torque equals mean torque 12000 Nm. Integrating the surplus torque gives energy fluctuation $\int2500\sin2\theta\,d\theta=-1250\cos2\theta$, with maximum-to-minimum difference 2500 J.
Speed coefficient is 0.005−(−0.005)=0.01. With ω=200×2π/60, $I=\Delta E/(C_s\omega^2)=569.93166$. **Answer: 570 kg m²**.