Power transmission and shaft sizing: compare diameters for equal power at different speeds Two circular shafts 'A' and 'B' transmit the same power. Shaft 'A' runs at 250 rpm and shaft 'B' runs at 300 rpm. Decide which shaft must have the larger diameter (same material and allowable shear stress assumed). Choose the correct statement.
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ATrue — shaft 'B' must have the greater diameter
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BFalse — shaft 'A' must have the greater diameter
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CTrue only if the materials of the shafts are different
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DCannot be determined without the exact power value
Answer
Correct Answer: False — shaft 'A' must have the greater diameter
Explanation
Given dataEqual power P is transmitted by shafts 'A' and 'B'.Speeds: NA = 250 rpm, NB = 300 rpm.Same material and allowable shear stress (design criterion).
Concept/ApproachPower P = T·ω, so torque T = P/ω. Lower speed ⇒ lower ω ⇒ higher T for the same power.For a solid circular shaft at allowable shear stress τ: T = (π/16)·τ·D³ ⇒ D ∝ T1/3.
Step-by-stepω ∝ N, thus TA/TB = ωB/ωA = NB/NA = 300/250 = 1.2.Therefore DA/DB = (TA/TB)1/3 ≈ (1.2)1/3 > 1.Hence shaft 'A' (slower) needs the larger diameter.
Common pitfallConfusing high speed with larger diameter; actually, for equal power, lower speed requires higher torque and thus a larger diameter.
Final AnswerFalse — shaft 'A' must have the greater diameter.