The ratio of SI units to CGS units of density is

Options

A. `10^(3)`
B. `10^(2)`
C. `10^(-2)`
D. `10^(-3)`

Explanation

To find the ratio of the SI units to CGS units of density, we will follow these steps:

### Step 1: Understand the Definition of Density
Density (σ) is defined as the mass (m) of an object divided by its volume (V):
\[ \sigma = \frac{m}{V} \]

### Step 2: Identify the SI Units of Density
In the SI system:
- The unit of mass (m) is kilograms (kg).
- The unit of volume (V) is cubic meters (m³).

Thus, the SI unit of density is:
\[ \text{Density (SI)} = \frac{\text{kg}}{\text{m}^3} \]

### Step 3: Identify the CGS Units of Density
In the CGS system:
- The unit of mass (m) is grams (g).
- The unit of volume (V) is cubic centimeters (cm³).

Thus, the CGS unit of density is:
\[ \text{Density (CGS)} = \frac{\text{g}}{\text{cm}^3} \]

### Step 4: Convert SI Units to CGS Units
To find the ratio, we need to express the SI unit in terms of CGS units:
- 1 kg = 1000 g = \( 10^3 \) g
- 1 m = 100 cm, therefore, \( 1 \text{ m}^3 = (100 \text{ cm})^3 = 10^6 \text{ cm}^3 \)

Thus, we can express the SI unit of density in CGS units:
\[ \text{Density (SI)} = \frac{10^3 \text{ g}}{10^6 \text{ cm}^3} = \frac{10^3}{10^6} \frac{\text{g}}{\text{cm}^3} = 10^{-3} \frac{\text{g}}{\text{cm}^3} \]

### Step 5: Calculate the Ratio of SI to CGS Units
Now, we can find the ratio of the SI unit of density to the CGS unit of density:
\[ \text{Ratio} = \frac{\text{Density (SI)}}{\text{Density (CGS)}} = \frac{10^{-3} \frac{\text{g}}{\text{cm}^3}}{\frac{\text{g}}{\text{cm}^3}} = 10^{-3} \]

### Final Answer
The ratio of SI units to CGS units of density is:
\[ \text{Ratio} = 10^{-3} \]

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