Two spherical balls each of mass 1kg are place 1 cm apart. Find the gravitational force of attraction between them.

Options

A. `6.67xx10^(-9)`
B. `6.67xx10^(-7)`
C. `6.67xx10^(-8)`
D. `6.67xx10^(-5)`

Answer

To find the gravitational force of attraction between two spherical balls, we can use Newton's law of universal gravitation, which states that the gravitational force (F) between two masses (m1 and m2) separated by a distance (r) is given by the formula:

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

Where:
- \( F \) is the gravitational force,
- \( G \) is the universal 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 objects,
- \( r \) is the distance between the centers of the two masses.

### Step 1: Identify the values
From the problem, we have:
- Mass of each ball, \( m_1 = m_2 = 1 \, \text{kg} \)
- Distance between the balls, \( r = 1 \, \text{cm} = 0.01 \, \text{m} \)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the gravitational force formula:

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

Substituting the known values:

\[ F = \frac{(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \cdot (1 \, \text{kg}) \cdot (1 \, \text{kg})}{(0.01 \, \text{m})^2} \]

### Step 3: Calculate \( r^2 \)
Calculating \( r^2 \):

\[ r^2 = (0.01 \, \text{m})^2 = 0.0001 \, \text{m}^2 \]

### Step 4: Substitute \( r^2 \) back into the formula
Now substituting \( r^2 \) back into the equation:

\[ F = \frac{(6.67 \times 10^{-11})}{0.0001} \]

### Step 5: Perform the calculation
Now, calculate the force:

\[ F = 6.67 \times 10^{-11} \div 0.0001 = 6.67 \times 10^{-11} \times 10^4 = 6.67 \times 10^{-7} \, \text{N} \]

### Final Answer
Thus, the gravitational force of attraction between the two spherical balls is:

\[ F = 6.67 \times 10^{-7} \, \text{N} \]

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