Shear stress to Max. Normal stress is 1:1. Ans B is correct because pour torsion is applied so shear stress is developed when we draw the mohr circle we find maximum shear stress is equal to maximum normal stress. This discussion on A solid circular shaft is subjected to pure torsion.

Maximum Shear Stress and Maximum Normal Stress in a Circular Shaft under Torsion

When a pure torsion moment is applied to a solid circular shaft, the shaft will experience both shear stress and normal stress. The maximum shear stress and maximum normal stress occur at different points on the shaft.

Maximum Shear Stress

The maximum shear stress occurs at the outer surface of the shaft, where the radius is maximum. This is because the shear stress is directly proportional to the distance from the axis of rotation. At the outer surface, the distance from the axis is maximum, and therefore the shear stress is maximum.

Maximum Normal Stress

The maximum normal stress occurs at the inner surface of the shaft, where the radius is minimum. This is because the normal stress is directly proportional to the distance from the neutral axis. At the inner surface, the distance from the neutral axis is minimum, and therefore the normal stress is maximum.

Ratio of Maximum Shear Stress to Maximum Normal Stress

As the maximum shear stress and maximum normal stress occur at different points on the shaft, the ratio of these stresses is not constant. However, at any point on the shaft, the ratio of maximum shear stress to maximum normal stress is always equal to 1 : 1. This is because the shear stress and normal stress are related by the following equation:

shear stress = normal stress x shear modulus / Young's modulus

As the shear modulus is equal to Young's modulus divided by 2(1 + Poisson's ratio), and Poisson's ratio is typically less than 0.5 for most materials, the shear modulus is always less than the Young's modulus. Therefore, the maximum shear stress is always less than the maximum normal stress, and the ratio of these stresses is always equal to 1 : 1.

Conclusion

In conclusion, when a solid circular shaft is subjected to a pure torsion moment, the maximum shear stress occurs at the outer surface of the shaft, while the maximum normal stress occurs at the inner surface. However, at any point on the shaft, the ratio of maximum shear stress to maximum normal stress is always equal to 1 : 1.