The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ and $${\sigma _3} = 0\,\,MPa.$$ The yield strength of the material is $$200$$ $$MPa.$$ The factor of safety calculated using Tresca (maximum shear stress) theory is $${n_T}$$ and the factor of safety calculated using Von Mises (maximum distortional energy) theory is $${n_V}$$. Which one of the following relations is TRUE?

A machine element is subjected to the following bi-axial state of stress: $$\,\,{\sigma _x} = 80MPa;\,\,{\sigma _y} = 20MPa;\,\,{\tau _{xy}} = 40MPa.$$ If the shear strength of the material is $$100 MPa,$$ the factor of safety as per Tresca’s maximum shear stress theory is

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The yield and ultimate strengths of the shaft material in tension are $$300$$ $$MPa$$ and $$450$$ $$MPa,$$ respectively. The factor of safety using maximum distortion energy (Von - Mises) theory is __________.

Consider the two states of stress as shown in configurations $${\rm I}$$ and $${\rm II}$$ in the figure below. From the standpoint of distortion energy (Von - Mises) criterion, which one of the following statements is true?