The acceleration due to gravitiy is `"9.8 ms"^(-2)`. Give its dimensional formula.

Options

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

Answer

To find the dimensional formula for the acceleration due to gravity, which is given as \(9.8 \, \text{m/s}^2\), we can follow these steps:

### Step 1: Understand the Units of Acceleration
Acceleration is defined as the change in velocity per unit time. The unit of acceleration is meters per second squared (\( \text{m/s}^2 \)).

### Step 2: Break Down the Units
The unit of acceleration can be expressed as:
\[ \text{Acceleration} = \frac{\text{Distance}}{\text{Time}^2} \]
Thus, we can write:
\[ \text{m/s}^2 = \frac{\text{m}}{\text{s}^2} \]

### Step 3: Identify the Dimensional Formulas
The dimensional formula for distance (length) is:
\[ [\text{Length}] = L \]
And the dimensional formula for time is:
\[ [\text{Time}] = T \]

### Step 4: Substitute the Dimensional Formulas
Substituting the dimensional formulas for meters and seconds into the expression for acceleration, we get:
\[ [\text{Acceleration}] = \frac{[\text{Length}]}{[\text{Time}]^2} = \frac{L}{T^2} \]

### Step 5: Write the Final Dimensional Formula
Thus, the dimensional formula for acceleration due to gravity is:
\[ [L T^{-2}] \]

### Step 6: Consider Mass Dimension
Since acceleration does not depend on mass, the dimensional formula can also be expressed including mass with an exponent of zero:
\[ [M^0 L T^{-2}] \]

### Conclusion
The final dimensional formula for the acceleration due to gravity is:
\[ M^0 L T^{-2} \]