The dimensional formula for moment of couple is

Options

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

Answer

To find the dimensional formula for the moment of a couple, we can follow these steps:

### Step 1: Understand the Concept of Moment of Couple
The moment of a couple is defined as the product of one of the forces and the perpendicular distance between the two forces. Mathematically, it can be expressed as:
\[ \text{Moment of Couple} = F \times d \]
where \( F \) is the force and \( d \) is the perpendicular distance between the forces.

### Step 2: Write the Expression for Moment of Couple
From the definition, we can write:
\[ \text{Moment of Couple} = F \times s \]
where \( s \) is the perpendicular distance.

### Step 3: Determine the Dimensional Formula for Force
The dimensional formula for force \( F \) is derived from Newton's second law, which states that force equals mass times acceleration:
\[ F = m \cdot a \]
The dimensional formula for mass \( m \) is \( [M] \) and for acceleration \( a \) (which is velocity per time) is:
\[ a = \frac{L}{T^2} \]
Thus, the dimensional formula for force becomes:
\[ [F] = [M][L][T^{-2}] = [M L T^{-2}] \]

### Step 4: Determine the Dimensional Formula for Distance
The dimensional formula for distance \( s \) is simply:
\[ [s] = [L] \]

### Step 5: Combine the Dimensional Formulas
Now, substituting the dimensional formulas for force and distance into the expression for the moment of couple:
\[ [\text{Moment of Couple}] = [F] \times [s] = [M L T^{-2}] \times [L] \]
This simplifies to:
\[ [\text{Moment of Couple}] = [M L^2 T^{-2}] \]

### Step 6: Conclusion
Thus, the dimensional formula for the moment of a couple is:
\[ [M L^2 T^{-2}] \]