The dimensional formula for areal velocity is

Options

A. `[M^(0)L^(-2)T]`
B. `[M^(0)L^(-2)T^(-1)]`
C. `[M^(0)L^(2)T^(-1)]`
D. `[M^(0)L^(2)T]`

Answer

To find the dimensional formula for areal velocity, we will follow these steps:

### Step 1: Understand Areal Velocity
Areal velocity is defined as the area covered per unit time. Mathematically, it can be expressed as:

\[ \text{Areal Velocity} = \frac{\Delta A}{\Delta t} \]

where \(\Delta A\) is the change in area and \(\Delta t\) is the change in time.

### Step 2: Determine the Dimensions of Area
The dimensional formula for area (A) is derived from the formula for area, which is length squared. Therefore, the dimensional formula for area is:

\[ [A] = L^2 \]

where \(L\) represents the dimension of length.

### Step 3: Determine the Dimensions of Time
The dimensional formula for time (t) is simply:

\[ [T] = T \]

### Step 4: Combine the Dimensions for Areal Velocity
Now, substituting the dimensions of area and time into the formula for areal velocity, we get:

\[ [\text{Areal Velocity}] = \frac{[A]}{[T]} = \frac{L^2}{T} \]

### Step 5: Write the Final Dimensional Formula
Thus, the dimensional formula for areal velocity is:

\[ [\text{Areal Velocity}] = L^2 T^{-1} \]

### Conclusion
The final answer for the dimensional formula of areal velocity is \(L^2 T^{-1}\).