If the density of substance is 'P' gcm³. Then its density in Sl system is

Options

A. 1000 P kg `m^(-3)`
B. 2000 P kg `m^(-3)`
C. 3000 P kg `m^(-3)`
D. 4000 P kg `m^(-3)`

Explanation

To convert the density of a substance from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given density**: The density of the substance is given as \( P \) g/cm³.

2. **Understand the conversion factors**:
- We know that 1 gram (g) is equal to \( \frac{1}{1000} \) kilograms (kg).
- We also know that 1 centimeter (cm) is equal to \( \frac{1}{100} \) meters (m).

3. **Convert grams to kilograms**:
- Since \( 1 \text{ g} = \frac{1}{1000} \text{ kg} \), we can express the density in kg as:
\[ P \text{ g/cm}^3 = P \times \frac{1}{1000} \text{ kg/cm}^3 \]

4. **Convert cubic centimeters to cubic meters**:
- Since \( 1 \text{ cm} = \frac{1}{100} \text{ m} \), then \( 1 \text{ cm}^3 = \left(\frac{1}{100} \text{ m}\right)^3 = \frac{1}{1000000} \text{ m}^3 \).
- Therefore, we can express the density in terms of m³ as:
\[ P \times \frac{1}{1000} \text{ kg/cm}^3 = P \times \frac{1}{1000} \times \frac{1000000}{1} \text{ kg/m}^3 \]

5. **Simplify the expression**:
- Now, simplifying the expression gives us:
\[ P \times \frac{1000000}{1000} \text{ kg/m}^3 = P \times 1000 \text{ kg/m}^3 \]

6. **Final result**:
- Thus, the density in SI units (kg/m³) is:
\[ 1000P \text{ kg/m}^3 \]

### Conclusion:
The density of the substance in the SI system is \( 1000P \) kg/m³.

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