Calculate the force of gravitation between the bodies , each of mass 100 kg and 1 m apart on the surface of the earth . Will the force of attraction be different if the same bodies are taken on the moon , their separation remaining constant ?

Answer

To calculate the force of gravitation between two bodies, we can use Newton's law of universal gravitation, which is given by the formula:

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

Where:
- \( F \) is the force of gravitation,
- \( G \) 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
Given:
- \( m_1 = 100 \, \text{kg} \)
- \( m_2 = 100 \, \text{kg} \)
- \( r = 1 \, \text{m} \)

### Step 2: Substitute the values into the formula
Substituting the values into the formula gives:

\[ F = \frac{6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \cdot 100 \, \text{kg} \cdot 100 \, \text{kg}}{(1 \, \text{m})^2} \]

### Step 3: Calculate the force
Calculating the force:

\[ F = \frac{6.67 \times 10^{-11} \cdot 10000}{1} \]
\[ F = 6.67 \times 10^{-7} \, \text{N} \]

### Step 4: Consider the scenario on the Moon
The force of gravitation between the two bodies depends only on their masses and the distance between them, as per the formula. The gravitational constant \( G \) remains the same regardless of the location (Earth or Moon). Therefore, even if the bodies are taken to the Moon, the force of attraction will remain the same because:
- The masses \( m_1 \) and \( m_2 \) are unchanged.
- The distance \( r \) remains constant at 1 meter.

### Final Answer
The force of gravitation between the two bodies is \( 6.67 \times 10^{-7} \, \text{N} \) and this force will not change if the bodies are taken to the Moon.

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