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 a Couple
A couple consists of two equal and opposite forces acting on an object, separated by a certain distance. The moment of a couple is defined as the product of one of the forces and the perpendicular distance between the lines of action of the forces.

### Step 2: Write the Formula for the Moment of a Couple
The moment of a couple (M) can be expressed as:
\[ M = F \times d \]
where:
- \( F \) is the force,
- \( d \) is the perpendicular distance between the two forces.

### Step 3: Determine the Dimensional Formula for Force
Force is defined by Newton's second law as:
\[ F = m \times a \]
where:
- \( m \) is mass, and its dimensional formula is \([M]\),
- \( a \) is acceleration, and its dimensional formula is \([L T^{-2}]\).

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

### Step 4: Determine the Dimensional Formula for Distance
The perpendicular distance \( d \) has the dimensional formula:
\[ [d] = [L] \]

### Step 5: Combine the Dimensional Formulas
Now, substituting the dimensional formulas of force and distance into the formula for the moment of a couple:
\[ [M] = [F] \times [d] = [M L T^{-2}] \times [L] \]

### Step 6: Simplify the Expression
Combining the dimensions gives:
\[ [M] = [M L^2 T^{-2}] \]

### Conclusion
The dimensional formula for the moment of a couple is:
\[ [M] = [M L^2 T^{-2}] \]