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 first need to understand what inertia represents. Inertia is the property of an object to resist changes in its state of motion, which means it is related to mass and motion.

### Step-by-Step Solution:

1. **Understanding Inertia**: Inertia is the resistance of any physical object to any change in its velocity. It is not a physical quantity like mass or force, but rather a property that describes how mass behaves in motion.

2. **Identifying the Relevant Quantity**: The inertia of an object is directly related to its mass. In classical mechanics, the inertia is often associated with mass, which is a measure of the amount of matter in an object.

3. **Dimensional Formula of Mass**: The dimensional formula for mass (m) is represented as [M]. It is the only quantity that directly relates to inertia.

4. **Inertia as a Non-Physical Quantity**: Since inertia itself is not a physical quantity but a property, it does not have a standard dimensional formula like other physical quantities such as force or energy.

5. **Dimensional Formula of Inertia**: Therefore, the dimensional formula of inertia can be expressed as:
\[ [I] = M^0 L^0 T^0 \]
This indicates that inertia does not depend on mass (M), length (L), or time (T) in a conventional sense.

6. **Conclusion**: The dimensional formula of inertia is \( M^0 L^0 T^0 \), which signifies that it is a dimensionless quantity.

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