If the value of universal gravitational constant is `6.67xx10^(11) Nm^2 kg^(-2),` then find its value in CGS system.

Explanation

To convert the universal gravitational constant \( G \) from the MKS system (SI units) to the CGS system, we follow these steps:

### Step 1: Understand the given values
We are given:
- \( G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)

### Step 2: Identify the units in both systems
In the MKS system:
- \( \text{N} \) (Newton) is the unit of force.
- \( \text{m} \) (meter) is the unit of length.
- \( \text{kg} \) (kilogram) is the unit of mass.

In the CGS system:
- \( \text{dyne} \) is the unit of force.
- \( \text{cm} \) (centimeter) is the unit of length.
- \( \text{g} \) (gram) is the unit of mass.

### Step 3: Convert the units
We need to convert the units from MKS to CGS:
- \( 1 \, \text{N} = 10^5 \, \text{dyne} \)
- \( 1 \, \text{m} = 100 \, \text{cm} \)
- \( 1 \, \text{kg} = 1000 \, \text{g} \)

### Step 4: Substitute the conversions into the equation
Using the relationship:
\[ N_1 U_1 = N_2 U_2 \]
where:
- \( N_1 = 6.67 \times 10^{-11} \)
- \( U_1 = \text{Nm}^2/\text{kg}^2 \)
- \( U_2 = \text{dyne cm}^2/\text{g}^2 \)

We can express \( U_1 \) in terms of CGS units:
\[ U_1 = \text{N} \cdot \text{m}^2/\text{kg}^2 = (10^5 \, \text{dyne}) \cdot (100 \, \text{cm})^2/(1000 \, \text{g})^2 \]

### Step 5: Calculate \( U_1 \) in CGS
Now substituting the conversions:
\[ U_1 = 10^5 \, \text{dyne} \cdot 10000 \, \text{cm}^2 / 1000000 \, \text{g}^2 \]
\[ U_1 = 10^5 \, \text{dyne} \cdot 10^{-2} \, \text{cm}^2/\text{g}^2 = 10^3 \, \text{dyne cm}^2/\text{g}^2 \]

### Step 6: Substitute back to find \( N_2 \)
Now we can find \( N_2 \):
\[ N_2 = \frac{N_1 U_1}{U_2} \]
Substituting the values:
\[ N_2 = \frac{6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2}{10^3 \, \text{dyne cm}^2/\text{g}^2} \]
\[ = 6.67 \times 10^{-11} \cdot \frac{10^5}{10^3} = 6.67 \times 10^{-11} \cdot 10^2 \]
\[ = 6.67 \times 10^{-9} \, \text{dyne cm}^2/\text{g}^2 \]

### Final Answer
Thus, the value of the universal gravitational constant \( G \) in the CGS system is:
\[ G = 6.67 \times 10^{-9} \, \text{dyne cm}^2/\text{g}^2 \]