The dimensional formula of inertia is

Options

A. `[M^1L^0T^0]`
B. `[M^1L^-1T^0]`
C. `[M^0L^0T^0]`
D. `[M^1L^0T^1]`

Answer

To find the dimensional formula of inertia, we need to understand what inertia is and how it relates to physical quantities.

### Step-by-Step Solution:

1. **Understanding Inertia**:
- Inertia is the property of a body to resist changes in its state of motion. It is not a measurable quantity like mass or velocity; instead, it describes a tendency.

2. **Inertia and Mass**:
- Although inertia itself is not a quantity that can be measured directly, it is often associated with mass. The greater the mass of an object, the greater its inertia. However, inertia itself does not have a specific value that can be compared.

3. **Dimensional Analysis**:
- In dimensional analysis, we represent physical quantities in terms of their basic dimensions: mass (M), length (L), and time (T).
- Since inertia is a property and not a measurable quantity, we can say that it does not have dimensions in the traditional sense.

4. **Conclusion on Dimensional Formula**:
- Therefore, the dimensional formula of inertia can be expressed as:
\[ [I] = M^0 L^0 T^0 \]
- This indicates that inertia is dimensionless.

5. **Final Answer**:
- The dimensional formula of inertia is \( M^0 L^0 T^0 \).