In a pure shear state of stress, where the shear stresses are \( \tau \), the coordinates of X and Y to draw the Mohr circle are: (A) \( \left.\mathrm{X} \epsilon_{x}, \tau\right), \mathrm{Y}\left(\sigma_{y}, \tau\right) \) (B) \( \mathrm{X}(\tau, 0), \mathrm{Y}(-\tau, 0) \) (C) \( \mathrm{X}(0, \tau), Y(0,-\tau) \) (D) \( \mathrm{X}(0,0), Y(\tau,-\tau) \)

For a pure shear state, the normal stresses are zero while the shear stress is τ (or -τ on the opposite face). The stress tensor then has:   σₓₓ = 0, σyy = 0, τ_xy = τ In Mohr’s circle, the coordinates for a stress element are plotted as (normal stress, shear stress) = (σ, τ). The center of the circle is given by the average of the normal stresses:   σ_avg = (σₓₓ + σyy) / 2 = (0 + 0)/2 = 0 and the radius R is:   R = √[ ((σₓₓ - σyy)/2)² + τ² ] = √(0 + τ²) = τ Thus, the Mohr circle is centered at (0, 0) with radius τ. Its intersection with the shear stress axis are at:   (0, +τ) and (0, -τ) These are the coordinates used to draw the Mohr circle. Comparing with the given options, option (C) "X(0, τ), Y(0, -τ)" correctly represents the coordinates. So, the answer is (C).