According to principal stress theory, the yield strength in shear (YSS) and the yield strength in tension (YST) are related to each other. The correct relation between YSS and YST is represented by option 'A', which states that YSS is equal to 0.5 times YST.

Explanation:
1. Principal Stress Theory: Principal stress theory is a theory used in material science and solid mechanics to determine the failure criteria of a material under different loading conditions. It states that failure occurs when the maximum principal stress reaches the yield strength of the material.

2. Yield Strength: Yield strength is the stress at which a material begins to deform plastically, i.e., it undergoes permanent deformation even after the removal of the applied load. It is an important parameter to determine the strength and reliability of a material.

3. Shear Stress and Tensile Stress: Shear stress is the stress that acts parallel to a given plane, while tensile stress is the stress that acts perpendicular to a given plane. In materials, shear stress and tensile stress can cause deformation and failure.

4. Relation between YSS and YST: According to the principal stress theory, the yield strength in shear (YSS) and the yield strength in tension (YST) are related to each other. The correct relation is given by option 'A', which states that YSS is equal to 0.5 times YST.

5. Explanation of Option 'A': In option 'A', YSS=0.5YST, it means that the yield strength in shear is half of the yield strength in tension. This implies that a material is more resistant to failure under shear stress compared to tensile stress. In other words, a material will reach its yield strength in tension before it reaches its yield strength in shear.

6. Significance of the Relation: The relation between YSS and YST is important in determining the failure criteria of a material under different loading conditions. It helps engineers and designers in selecting appropriate materials for specific applications based on their ability to withstand shear and tensile stresses.

In conclusion, according to principal stress theory, the correct relation between yield strength in shear (YSS) and yield strength in tension (YST) is represented by option 'A', which states that YSS is equal to 0.5 times YST. This relation indicates that a material is more resistant to failure under shear stress compared to tensile stress.

If (σ)1 is tensil stress then shear will be (σ)1/2
therefore YST =.5yss