The force of attraction between two bodies of masses 100 kg and 1000 Kg separated by a distance of 10 m is

Options

A. `6.67xx10^(-7)N`
B. `6.67xx10^(-8)N`
C. `6.67xx10^(-9)N`
D. `6.67xx10^(-10)`

Explanation

To find the force of attraction between two bodies of masses 100 kg and 1000 kg separated by a distance of 10 m, we can use Newton's law of universal gravitation. The formula is given by:

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

Where:
- \( F \) is the gravitational force between the two masses,
- \( G \) is the gravitational constant, approximately \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( m_1 \) and \( m_2 \) are the masses of the two bodies,
- \( r \) is the distance between the centers of the two masses.

### Step 1: Identify the values
- \( m_1 = 100 \, \text{kg} \)
- \( m_2 = 1000 \, \text{kg} \)
- \( r = 10 \, \text{m} \)

### Step 2: Substitute the values into the formula
\[ F = G \frac{m_1 m_2}{r^2} \]
Substituting the known values:
\[ F = 6.67 \times 10^{-11} \frac{100 \times 1000}{10^2} \]

### Step 3: Calculate \( r^2 \)
\[ r^2 = 10^2 = 100 \]

### Step 4: Calculate \( m_1 m_2 \)
\[ m_1 m_2 = 100 \times 1000 = 100000 \]

### Step 5: Substitute back into the equation
\[ F = 6.67 \times 10^{-11} \frac{100000}{100} \]

### Step 6: Simplify the fraction
\[ \frac{100000}{100} = 1000 \]
Thus,
\[ F = 6.67 \times 10^{-11} \times 1000 \]

### Step 7: Perform the multiplication
\[ F = 6.67 \times 10^{-8} \, \text{N} \]

### Final Answer
The force of attraction between the two bodies is:
\[ F = 6.67 \times 10^{-8} \, \text{N} \]