Q$4)$ A point on a thin plate is subjected to the stresses as shown in FigQ$4.$The stresses on a certain

plane $\text{'}p\text{'}$ are $90$MPa tensile and $40$ MPa shear whereas on another plane $\text{'}q\text{'}$ are $60$MPa

tensile and $30$MPa shear respectively.

a$)$ Draw the Mohr's circle for the given state of stress at a point.

b$)$ Determine the principal planes and the principal stresses with the help of Mohr's circle.

c$)$ Determine the angle $\text{'}\text{'}$ between the plane $\text{'}p\text{'}$ and plane $\text{'}q\text{'}.$