The density of aluminium in S.I. system is 2700 kg `m^(-3)` . Find its value in C.G.S. System.

Options

A. 1.7 g `m^(-3)`
B. 2.7 g `m^(-3)`
C. 3.7 g `m^(-3)`
D. 4.7 g `m^(-3)`

Explanation

To convert the density of aluminum from the SI system to the CGS system, we will follow these steps:

### Step 1: Understand the given density in SI units
The density of aluminum is given as:
\[ \text{Density (SI)} = 2700 \, \text{kg/m}^3 \]

### Step 2: Convert kilograms to grams
In the CGS system, mass is measured in grams. We know that:
\[ 1 \, \text{kg} = 1000 \, \text{g} \]
Thus, to convert 2700 kg to grams:
\[ 2700 \, \text{kg} = 2700 \times 1000 \, \text{g} = 2700000 \, \text{g} \]

### Step 3: Convert cubic meters to cubic centimeters
In the CGS system, volume is measured in cubic centimeters. We know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \]
Therefore, to convert cubic meters to cubic centimeters:
\[ 1 \, \text{m}^3 = (100 \, \text{cm})^3 = 1000000 \, \text{cm}^3 \]

### Step 4: Calculate the density in CGS units
Now, we can calculate the density in CGS units:
\[ \text{Density (CGS)} = \frac{\text{mass in grams}}{\text{volume in cubic centimeters}} = \frac{2700000 \, \text{g}}{1000000 \, \text{cm}^3} \]
\[ \text{Density (CGS)} = 2.7 \, \text{g/cm}^3 \]

### Final Answer
The density of aluminum in the CGS system is:
\[ \text{Density} = 2.7 \, \text{g/cm}^3 \]

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