$3.$

a$)$ Prove that a point on Mohr's circle represents the magnitude and direction of normal and shear stresses on any randomly oriented plane?

b$)$ Derive the expressions for shear and normal stresses at a point, considering the plane stress condition.

c$.$ Draw curves that depict the variation of normal and shear stresses on oblique plane at given orientation. Also write down the major conclusions you can draw.