Q1: If p₁ and p₂ are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle θ^° to the principal plane carrying the principal stress p₁, is :

ANS:C -

To determine the normal stress on a plane inclined at an angle θ to the principal plane carrying the principal stress p1​, we can use Mohr's circle and the concept of stress transformation. Given that p1​ and p2​ are mutually perpendicular principal stresses, we can represent them as the major and minor principal stresses, respectively, on the Mohr's circle. The normal stress σn​ on a plane inclined at an angle θ to the principal plane carrying the principal stress p1​ can be calculated using the formula for stress transformation: σn​=p1​+p2/2​​+p1​−p2/2 ​​cos(2θ) Where:

• p1​ = Major principal stress
• p2​ = Minor principal stress
• σn​ = Normal stress on the inclined plane
• θ = Angle of inclination of the plane to the principal plane carrying p1​

In this formula, the first term p1​+p2​​ /2represents the average stress on the plane due to the two principal stresses, and the second term p1​−p2/2 ​​cos(2θ) represents the additional stress due to the inclination of the plane. Therefore, the normal stress on any plane inclined at an angle θ to the principal plane carrying the principal stress p1​ is given by the formula above.