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.

Given data
Equal power P is transmitted by shafts 'A' and 'B'.Speeds: N_A = 250 rpm, N_B = 300 rpm.Same material and allowable shear stress (design criterion).

Concept/Approach
Power 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 ∝ T^1/3.

Step-by-step
ω ∝ N, thus T_A/T_B = ω_B/ω_A = N_B/N_A = 300/250 = 1.2.Therefore D_A/D_B = (T_A/T_B)^1/3 ≈ (1.2)^1/3 > 1.Hence shaft 'A' (slower) needs the larger diameter.

Common pitfall
Confusing high speed with larger diameter; actually, for equal power, lower speed requires higher torque and thus a larger diameter.

Final Answer
False — shaft 'A' must have the greater diameter.