According to the question, we need to determine how the shear stress for a circular shaft due to torque varies. The correct answer is option 'D', which states that the shear stress varies from the center to the surface linearly.

To understand why this is the correct answer, let's break down the concept of shear stress in a circular shaft and how it is affected by torque.

1. Shear Stress in a Circular Shaft:
- When a torque is applied to a circular shaft, it creates shear stress in the material.
- Shear stress is defined as the force per unit area parallel to the cross-sectional area of the shaft.
- In a circular shaft, the shear stress is highest at the outer surface and decreases towards the center.

2. Variation of Shear Stress due to Torque:
- When a torque is applied to a circular shaft, the shear stress distribution is not uniform across the cross-section.
- The shear stress is maximum at the outer surface and decreases towards the center of the shaft.
- This variation in shear stress can be represented by a linear or parabolic distribution.

3. Linear Variation of Shear Stress:
- In a circular shaft, the shear stress can vary linearly from the center to the surface due to torque.
- This means that the shear stress at any point along the radius of the shaft can be calculated using a linear equation.
- The linear variation is a simple and commonly used approximation for many engineering calculations.

4. Parabolic Variation of Shear Stress:
- In some cases, the shear stress distribution in a circular shaft can be assumed to vary parabolically from the center to the surface.
- However, this assumption is not applicable in the case of shear stress due to torque.
- The parabolic variation is more commonly used to represent the distribution of bending stress in beams.

In conclusion, the shear stress for a circular shaft due to torque varies from the center to the surface linearly. This linear variation is a simple and widely accepted approximation for engineering calculations. The parabolic variation, although commonly used for bending stress in beams, is not applicable in this case.