GATE 2023 ME – Question 60
A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 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 off to two decimal places)
Take $\pi = 3.14$.
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Show answer and explanation
Correct answer: 237.69 to 240.07
Explanation
The angle of twist is $\theta = \frac{TL}{GJ}$, so $T = \frac{GJ\theta}{L}$. The polar moment is $J = \frac{\pi d^4}{32} = \frac{3.14 \times 0.1^4}{32} = 9.8125 \times 10^{-6}$ m$^4$ and $\theta = 0.5° = \frac{0.5 \times 3.14}{180} = 0.008722$ rad. Then $T = \frac{80 \times 10^9 \times 9.8125 \times 10^{-6} \times 0.008722}{1.5} = 4564.6$ N m. The angular speed is $\omega = \frac{2\pi \times 500}{60} = 52.33$ rad/s, so the power is $T\omega = 4564.6 \times 52.33 = 238{,}882$ W $= 238.88$ kW.