Q1: The maximum shear stress occurs on the filament which makes an angle with the horizontal plane equal to

ANS:B - 45°

Shear stress in a soil mass subjected to principal stress,
P1 and P2, = {(P1-P2)/2}*Sin2a.

Where a is the angle of the failure plane with the horizontal.

For "a" = 45, Sin will give max value and hence we will obtain max shear stress. According to Mohr's circle;

The critical angle is 45+ π by 2.

For cohesion, soil π is zero.

Then the angle between the horizontal plane and shear stress is 45. Shear Stress= (P1-P2)/2 * Sin 2a,
For a = 45 , Shear Stress is max.
i.e. (P1-P2)/2.