A two-dimensional fluid element rotates like a rigid body, and at a point within the element, the pressure is 1 unit. What is the radius of Mohr's circle, characterising the state of stress at that point?

Explanation:

Concept:

Mohr's circle is a graphical method which gives the relation between normal stresses and shear stress acting at a point in a body at an inclined plane. For the 2D state of stress, Mohr's circle is:

Calculation: 

• In this case, equal pressure is acting from all directions on fluid element (hydrodynamic state of stress).
• So, normal stresses are equal in all directions on the fluid element and shear stress is zero.
• The principal stresses are equal in magnitude and compressive in nature.
• The Mohr's circle is a point on the negative \(\sigma\) - axis.

\(\therefore\) The radius of Mohr's circle is zero. 

Thus, option (2) is the correct answer.