The dimensional formula `ML^2T^(-2)` represents

Options

A. Moment of a force
B. Force
C. Acceleration
D. Momentum

Answer

To determine what the dimensional formula `ML^2T^(-2)` represents, we can follow these steps:

### Step 1: Understand the given dimensional formula
The dimensional formula given is `ML^2T^(-2)`. Here, `M` represents mass, `L` represents length, and `T` represents time.

### Step 2: Analyze the options
We need to identify physical quantities that correspond to the dimensional formula `ML^2T^(-2)`. Common candidates include:
- Moment of a force (torque)
- Work or energy
- Pressure

### Step 3: Calculate the dimensional formula for moment of a force
The moment of a force (or torque) about a point is calculated as:
\[ \text{Moment} = \text{Force} \times \text{Distance} \]

### Step 4: Find the dimensional formula for force
The dimensional formula for force (F) is given by:
\[ F = m \cdot a \]
Where:
- \( m \) is mass (M)
- \( a \) is acceleration, which has the dimensional formula \( L^1T^{-2} \)

Thus, the dimensional formula for force is:
\[ F = M^1L^1T^{-2} \]

### Step 5: Find the dimensional formula for distance
The dimensional formula for distance (D) is:
\[ D = L^1 \]

### Step 6: Combine the formulas
Now, substituting the dimensional formulas into the moment of a force:
\[ \text{Moment} = F \times D = (M^1L^1T^{-2}) \times (L^1) \]

This gives us:
\[ \text{Moment} = M^1L^{1+1}T^{-2} = M^1L^2T^{-2} \]

### Step 7: Conclusion
Thus, the dimensional formula `ML^2T^(-2)` corresponds to the moment of a force.

### Final Answer
The dimensional formula `ML^2T^(-2)` represents the moment of a force.

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