The gravitational force acting on a particle of 1 g due to a similar particle is equal to `6.67xx10^-17 N`. Calculate the separation between the particles.

Explanation

To solve the problem of finding the separation between two particles of mass 1 g each, given the gravitational force acting between them is \(6.67 \times 10^{-17} \, \text{N}\), we can use Newton's law of universal gravitation. Here's the step-by-step solution:

### Step 1: Write down the formula for gravitational force.
The gravitational force \(F\) between two masses \(m_1\) and \(m_2\) separated by a distance \(r\) is given by the formula:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \(G\) is the gravitational constant.

### Step 2: Identify the values.
In this case:
- \(m_1 = m_2 = 1 \, \text{g} = 1 \times 10^{-3} \, \text{kg}\)
- \(F = 6.67 \times 10^{-17} \, \text{N}\)
- \(G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\)

### Step 3: Substitute the values into the formula.
Substituting the known values into the gravitational force equation:
\[ 6.67 \times 10^{-17} = \frac{6.67 \times 10^{-11} \cdot (1 \times 10^{-3}) \cdot (1 \times 10^{-3})}{r^2} \]

### Step 4: Simplify the equation.
This simplifies to:
\[ 6.67 \times 10^{-17} = \frac{6.67 \times 10^{-11} \cdot 10^{-6}}{r^2} \]
\[ 6.67 \times 10^{-17} = \frac{6.67 \times 10^{-17}}{r^2} \]

### Step 5: Solve for \(r^2\).
Now, we can cancel \(6.67 \times 10^{-17}\) from both sides:
\[ 1 = \frac{1}{r^2} \]

### Step 6: Find \(r\).
Taking the reciprocal gives:
\[ r^2 = 1 \]
Taking the square root of both sides:
\[ r = 1 \, \text{m} \]

### Conclusion
The separation between the two particles is \(1 \, \text{meter}\).

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