(a) Comparison by strength: Assume that both the shaft have same length, material, same weight and hence the same maximum shear stress. Let,
DS = Diameter of the solid shaft.
DH = External Diameter of the Hollow shaft
dH = Internal diameter of the hollow shaft
AS = Cross sectional Area of solid shaft
AH = Cross-sectional area of hollow shaft
TS = Torque transmitted by the solid shaft
TH = Torque transmitted by the hollow shaft
TH /TS = 1.44
This show that the torque transmitted by the hollow shaft is greater than the solid shaft, thereby proving that the hollow shaft is stronger than the solid shaft.
(b) Comparison by weight: Assume that both the shaft have same length, material, Now if the torque applied to both shafts is same, then the maximum shear stress will also be same in both the cases.
Let WH = Weight of hollow shaft
WS = Weight of Solid shaft
Then, WH/WS = AH/AS
WH/WS = 0.7829