Force `xx` velocity `=x`. The dimensional formula of `x` is

Options

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

Answer

To find the dimensional formula of \( x \) given that \( \text{Force} \times \text{Velocity} = x \), we will follow these steps:

### Step 1: Write down the formula for \( x \)
We know from the question that:
\[ x = \text{Force} \times \text{Velocity} \]

### Step 2: Find the dimensional formula of Force
The dimensional formula for Force is given by:
\[ \text{Force} = \text{mass} \times \text{acceleration} = M \cdot \left( \frac{L}{T^2} \right) = MLT^{-2} \]

### Step 3: Find the dimensional formula of Velocity
The dimensional formula for Velocity is:
\[ \text{Velocity} = \frac{\text{displacement}}{\text{time}} = \frac{L}{T} = LT^{-1} \]

### Step 4: Combine the dimensional formulas
Now, we can combine the dimensional formulas of Force and Velocity:
\[ x = \text{Force} \times \text{Velocity} = (MLT^{-2}) \times (LT^{-1}) \]

### Step 5: Perform the multiplication
Now we multiply the two dimensional formulas:
\[ x = M \cdot L \cdot T^{-2} \cdot L \cdot T^{-1} = M \cdot L^2 \cdot T^{-3} \]

### Step 6: Write the final dimensional formula
Thus, the dimensional formula of \( x \) is:
\[ \text{Dimensional formula of } x = ML^2T^{-3} \]

### Conclusion
From the options provided, we can conclude that the correct option is \( ML^2T^{-3} \).

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