Final answer:
The average shear stress in a square key transmitting torque T with side d/4 and length l is calculated as 16T/ld², making the correct answer B. 16T/ld².
Step-by-step explanation:
The student's question pertains to the average shear stress that develops in a square key used to transmit torque between a shaft and a pulley.
To calculate this shear stress, a few mechanical concepts come into play such as torque, shear force, and cross-sectional area.
Shear stress (usually denoted as τ) is defined as the shear force F applied perpendicular to the cross-sectional area A, which for a square key with side d/4 would be
(d/4) × (d/4) = d²/16.
Since the torque T is transmitted by the key, the shear force F is equal to the torque T divided by the radial distance from the center, which in this case would be d/2.
Therefore, the average shear stress τ is given by the formula:
τ = F/A = (4T/d)/(d²/16) = 16T/ld²
Hence, the correct answer to the question is B. 16T/ld².