Find the dimensional formula of volumetric stress.

Answer

To find the dimensional formula of volumetric stress, we will follow these steps:

### Step 1: Understand the Definition of Volumetric Stress
Volumetric stress is defined as the force applied per unit area. It can be expressed mathematically as:
\[ \text{Volumetric Stress} = \frac{\text{Force}}{\text{Area}} \]

### Step 2: Write the Dimensional Formula for Force
The force (F) can be expressed in terms of mass (m) and acceleration (a):
\[ F = m \cdot a \]
The dimensional formula for mass (m) is \([M]\) and for acceleration (a) is \([L T^{-2}]\). Therefore, the dimensional formula for force is:
\[ [F] = [M][L T^{-2}] = [M L T^{-2}] \]

### Step 3: Write the Dimensional Formula for Area
The area (A) is defined as length squared:
\[ A = L^2 \]
Thus, the dimensional formula for area is:
\[ [A] = [L^2] \]

### Step 4: Combine the Dimensional Formulas
Now, substituting the dimensional formulas of force and area into the formula for volumetric stress:
\[ \text{Volumetric Stress} = \frac{[F]}{[A]} = \frac{[M L T^{-2}]}{[L^2]} \]

### Step 5: Simplify the Expression
Now, we simplify the expression:
\[ \text{Volumetric Stress} = \frac{[M L T^{-2}]}{[L^2]} = [M L^{1-2} T^{-2}] = [M L^{-1} T^{-2}] \]

### Conclusion
The dimensional formula for volumetric stress is:
\[ \text{Dimensional Formula of Volumetric Stress} = [M L^{-1} T^{-2}] \]