The dimensional formula of relative density is

Options

A. `ML^(-3)`
B. `LT^(-1)`
C. `MLT^(-2)`
D. Dimensionless

Answer

To find the dimensional formula of relative density, we can follow these steps:

### Step 1: Understand the Definition of Relative Density
Relative density (RD) is defined as the ratio of the density of a substance to the density of water. Mathematically, it can be expressed as:
\[ \text{Relative Density (RD)} = \frac{\text{Density of Substance}}{\text{Density of Water}} \]

### Step 2: Write the Formula for Density
Density is defined as mass per unit volume. The formula for density (\( \rho \)) is:
\[ \rho = \frac{m}{V} \]
Where:
- \( m \) is mass (with dimensional formula [M])
- \( V \) is volume (with dimensional formula [L³])

### Step 3: Determine the Dimensional Formula for Density
From the formula for density, we can derive its dimensional formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{[M]}{[L^3]} = [M L^{-3}] \]

### Step 4: Apply the Dimensional Formula to Relative Density
Since relative density is the ratio of two densities, we can substitute the dimensional formula of density into the relative density formula:
\[ \text{Relative Density} = \frac{[M L^{-3}]}{[M L^{-3}]} \]

### Step 5: Simplify the Expression
When we divide the same dimensional formula by itself, we get:
\[ \text{Relative Density} = 1 \]
This indicates that relative density is a dimensionless quantity.

### Conclusion
Thus, the dimensional formula of relative density is dimensionless.

### Final Answer
The dimensional formula of relative density is **dimensionless**.

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