A sphere of mass 20 kg is attached by another sphere of mass 10 kg when their centres are 20 cm apart , with a force of `3.3 xx 10^(-7)`N . Calculate the constant of gravitation .

Answer

To solve the problem of finding the gravitational constant \( G \) given the masses of two spheres and the force between them, we can follow these steps:

### Step 1: Understand the given data
- Mass of the first sphere, \( m_1 = 20 \, \text{kg} \)
- Mass of the second sphere, \( m_2 = 10 \, \text{kg} \)
- Distance between the centers of the spheres, \( d = 20 \, \text{cm} = 0.20 \, \text{m} \)
- Gravitational force between the spheres, \( F = 3.3 \times 10^{-7} \, \text{N} \)

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

### Step 3: Rearrange the formula to solve for \( G \)
We can rearrange the formula to solve for \( G \):
\[ G = \frac{F \cdot d^2}{m_1 \cdot m_2} \]

### Step 4: Substitute the known values into the formula
Now we substitute the known values into the rearranged formula:
- \( F = 3.3 \times 10^{-7} \, \text{N} \)
- \( m_1 = 20 \, \text{kg} \)
- \( m_2 = 10 \, \text{kg} \)
- \( d = 0.20 \, \text{m} \)

Calculating \( d^2 \):
\[ d^2 = (0.20)^2 = 0.04 \, \text{m}^2 \]

Now substituting into the formula:
\[ G = \frac{(3.3 \times 10^{-7}) \cdot (0.04)}{20 \cdot 10} \]

### Step 5: Calculate the denominator
Calculating the denominator:
\[ 20 \cdot 10 = 200 \, \text{kg}^2 \]

### Step 6: Calculate \( G \)
Now substituting back into the equation:
\[ G = \frac{(3.3 \times 10^{-7}) \cdot (0.04)}{200} \]
Calculating the numerator:
\[ 3.3 \times 10^{-7} \cdot 0.04 = 1.32 \times 10^{-8} \]

Now substituting this value into the equation for \( G \):
\[ G = \frac{1.32 \times 10^{-8}}{200} \]

Calculating \( G \):
\[ G = 6.6 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \]

### Final Answer
The gravitational constant \( G \) is:
\[ G = 6.6 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \]