Suppose force = n `xx` velocity then the diemsional formula of n is

Options

A. `M^(0)L^(0)T^(0)`
B. `ML^(0)T^(-1)`
C. `MLT^(-1)`
D. `ML^(-1)T^(-1)`

Explanation

To find the dimensional formula of \( n \) in the equation \( \text{Force} = n \times \text{Velocity} \), we can follow these steps:

### Step 1: Write down the relationship
Given the equation:
\[ \text{Force} = n \times \text{Velocity} \]

### Step 2: Rearrange the equation to solve for \( n \)
We can rearrange the equation to express \( n \) in terms of force and velocity:
\[ n = \frac{\text{Force}}{\text{Velocity}} \]

### Step 3: Write the dimensional formula for force
The dimensional formula for force \( F \) is given by:
\[ [F] = M L T^{-2} \]
where:
- \( M \) is mass,
- \( L \) is length,
- \( T \) is time.

### Step 4: Write the dimensional formula for velocity
The dimensional formula for velocity \( v \) is given by:
\[ [v] = L T^{-1} \]

### Step 5: Substitute the dimensional formulas into the equation for \( n \)
Now, substituting the dimensional formulas into the equation for \( n \):
\[ [n] = \frac{[F]}{[v]} = \frac{M L T^{-2}}{L T^{-1}} \]

### Step 6: Simplify the expression
Now we simplify the expression:
\[ [n] = \frac{M L T^{-2}}{L T^{-1}} = M T^{-2} \cdot T = M T^{-1} \]

### Step 7: Write the final dimensional formula for \( n \)
Thus, the dimensional formula for \( n \) is:
\[ [n] = M^1 L^0 T^{-1} \]

### Final Answer
The dimensional formula of \( n \) is:
\[ M^1 L^0 T^{-1} \]

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