The dimension of torque is:

Options

A. `[MT^(-2)]`
B. `[ML^(-1)T^(-1)]`
C. `[ML^(2)T^(-2)]`
D. `[ML^(3)T^(-3)]`

Explanation

To find the dimension of torque, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Torque**:
Torque (τ) is defined as the product of force (F) and the perpendicular distance (r) from the axis of rotation to the line of action of the force. Mathematically, this is expressed as:
\[ \tau = F \cdot r \]

2. **Determine the Dimensions of Force**:
The dimension of force can be derived from Newton's second law, which states that force is mass times acceleration. Thus:
\[ F = m \cdot a \]
where:
- Mass (m) has the dimension \( [M] \)
- Acceleration (a) has the dimension \( [L T^{-2}] \) (since acceleration is change in velocity over time).

Therefore, the dimension of force is:
\[ [F] = [M][L T^{-2}] = M L T^{-2} \]

3. **Determine the Dimensions of Distance**:
The dimension of distance (r) is simply:
\[ [r] = [L] \]

4. **Combine the Dimensions to Find Torque**:
Now, substituting the dimensions of force and distance into the torque formula:
\[ [\tau] = [F] \cdot [r] = (M L T^{-2}) \cdot [L] \]
This simplifies to:
\[ [\tau] = M L^2 T^{-2} \]

5. **Final Result**:
The dimension of torque is:
\[ [\tau] = M L^2 T^{-2} \]

### Conclusion:
The dimension of torque is \( M L^2 T^{-2} \).

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