The force with which the erth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data: The universal constant of gravitastion `G=6.67xx10^-11 N-m^2/kg^2` mass of the moon `=7.36xx10^22 ` kg, mass of the earth `=6xx10^24` kg and the distasnce between the earth and the `moon=3.8xx10^5` km.

Explanation

To calculate the weight of the moon using the given data, we can use the formula for gravitational force:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

Where:
- \( F \) is the gravitational force (weight of the moon in this case),
- \( G \) is the universal gravitational constant,
- \( m_1 \) is the mass of the moon,
- \( m_2 \) is the mass of the Earth,
- \( r \) is the distance between the centers of the two masses.

### Step 1: Convert Distance to Meters
The distance between the Earth and the moon is given in kilometers. We need to convert this to meters.

\[ r = 3.8 \times 10^5 \text{ km} = 3.8 \times 10^5 \times 1000 \text{ m} = 3.8 \times 10^8 \text{ m} \]

### Step 2: Substitute Values into the Formula
Now we can substitute the values into the gravitational force formula. We have:

- \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
- \( m_1 = 7.36 \times 10^{22} \, \text{kg} \) (mass of the moon)
- \( m_2 = 6 \times 10^{24} \, \text{kg} \) (mass of the Earth)
- \( r = 3.8 \times 10^8 \, \text{m} \)

The formula becomes:

\[ F = \frac{(6.67 \times 10^{-11}) \cdot (7.36 \times 10^{22}) \cdot (6 \times 10^{24})}{(3.8 \times 10^8)^2} \]

### Step 3: Calculate the Denominator
Calculate \( r^2 \):

\[ (3.8 \times 10^8)^2 = 3.8^2 \times (10^8)^2 = 14.44 \times 10^{16} = 1.444 \times 10^{17} \]

### Step 4: Calculate the Numerator
Now calculate the numerator:

\[ (6.67 \times 10^{-11}) \cdot (7.36 \times 10^{22}) \cdot (6 \times 10^{24}) \]

Calculating step by step:

1. \( 6.67 \times 7.36 = 49.1892 \)
2. \( 49.1892 \times 6 = 295.1352 \)
3. Now include the powers of ten:
\[ 295.1352 \times 10^{(-11 + 22 + 24)} = 295.1352 \times 10^{35} \]

### Step 5: Final Calculation
Now substitute back into the formula:

\[ F = \frac{295.1352 \times 10^{35}}{1.444 \times 10^{17}} \]

Calculating this gives:

\[ F \approx 20.4 \times 10^{18} \text{ N} = 2.04 \times 10^{19} \text{ N} \]

### Final Answer
Thus, the weight of the moon is approximately:

\[ \text{Weight of the moon} = 2.03 \times 10^{20} \text{ N} \]