Question

A metallic square plate is subjected to a uniform hydrostatic pressure (\(P\)). Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below. For the Mohr's circle, normal stress is positive towards the right and shear stress is positive in the upward direction.

• A.
• B.
• C.
• D.

Hint:

In cases of hydrostatic pressure, Mohr’s Circle is represented as a point on the normal stress axis with zero shear stress. The normal stress will be equal to the applied pressure.

Answer 1

The Correct Option is B

Step 1: Understand Hydrostatic Pressure and its Effect on Mohr's Circle
A uniform hydrostatic pressure \( P \) means that the stress is the same in all directions (isotropic stress).
This implies that the normal stress at every point is equal to the applied pressure, and there is no shear stress in this case.
Hydrostatic pressure can be represented on Mohr's Circle as a single point on the normal stress axis. The shear stress is zero, so the radius of the Mohr's Circle is zero.

Step 2: Identify the Key Characteristics of Mohr's Circle
In Mohr's Circle, the center of the circle lies at the normal stress value. For hydrostatic pressure, the normal stress is equal to \( P \), and the shear stress is zero.
This means Mohr's Circle will be a point on the normal stress axis, with the point located at \( P \) (since the radius is zero).

Step 3: Choose the Correct Mohr's Circle
Looking at the given options, we can eliminate options that do not match the characteristics of a hydrostatic pressure Mohr's Circle.
Option (B) correctly shows the Mohr's Circle with the center at \( P \), no shear stress, and a point on the normal stress axis.

Thus, the correct answer is (B).