The maximum shear stress in a solid shaft:
- The maximum shear stress in a solid shaft can be determined using the torsion formula:

τ = (T*r) / (J)

Where:
τ = maximum shear stress
T = twisting moment
r = radius of the shaft
J = polar moment of inertia

- The polar moment of inertia for a solid shaft is given by:

J = (π*D^4) / 32

Where:
D = diameter of the shaft

- Substituting the value of J in the torsion formula, we get:

τ = (T*r) / ((π*D^4) / 32)

The maximum shear stress in a hollow shaft:
- To find the maximum shear stress in a hollow shaft, we need to determine the polar moment of inertia for the hollow section.

- The polar moment of inertia for a hollow shaft is given by:

J = (π/32) * (D_o^4 - D_i^4)

Where:
D_o = outside diameter of the shaft
D_i = inside diameter of the shaft

- Substituting the value of J in the torsion formula, we get:

τ = (T*r) / ((π/32) * (D_o^4 - D_i^4))

Comparison between solid and hollow shaft:
- Let's compare the maximum shear stress in the solid and hollow shafts.

- For the solid shaft, the diameter D remains the same. But for the hollow shaft, we have the outside diameter D_o and inside diameter D_i.

- If we replace the solid shaft with a hollow shaft of outside diameter D and inside diameter D/2, the values for D_o and D_i can be determined as follows:

D_o = D
D_i = D/2

- Substituting these values in the hollow shaft torsion formula, we get:

τ = (T*r) / ((π/32) * (D^4 - (D/2)^4))

- Simplifying further, we can write:

τ = (T*r) / ((π/32) * (15/16) * D^4)

- Comparing this with the solid shaft torsion formula, we can see that the only difference is the factor of (15/16) in the hollow shaft formula.

Conclusion:
- Therefore, the maximum shear stress in the hollow shaft is reduced by a factor of (15/16) compared to the solid shaft when the outside diameter is D and the inside diameter is D/2.