The assumptions made in the theory of torsion are as under
1. The material of the shaft is homogeneous, isotropic and perfectly elastic.
2. The material obey's Hooke's law and the stress remains within limit of proportionality.
3. The twisting couples acts in the transverse plane only.
4. All radii remain straight after torsion.

Correct option is D

All four listed assumptions are made in the theory of torsion. These assumptions simplify the analysis of torsional stresses and strains in shafts under torsion and are widely accepted in mechanics of materials.
Important Key Points:
1. Homogeneous, isotropic, and perfectly elastic material:
· The material is assumed to have uniform properties (homogeneous) and behaves the same in all directions (isotropic).
· It follows the principles of elasticity, ensuring accurate stress-strain relationships.
2. Material obeys Hooke's law:
· Stress is directly proportional to strain within the proportionality limit, ensuring the linear relationship between stress and strain.
3. Twisting couples act in the transverse plane only:
· The torque or twisting moment acts perpendicular to the shaft's longitudinal axis, ensuring no axial or bending effects influence the torsion.
4. All radii remain straight after torsion:
· After torsion, the cross-sections of the shaft remain planar, and the radial lines (radii) do not warp or deform, which simplifies the analysis.