Two identical spheres of radius 2 cm and mass 1 kg are placed 1 cm apart on the surface of the earth. Then,

Options

A. the two spheres move towards each other.
B. the two spheres move away from each other.
C. there is no force of attraction between the two spheres.
D. None of these

Answer

To solve the problem, we need to analyze the gravitational interaction between the two identical spheres placed 1 cm apart on the surface of the Earth. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Setup
- We have two identical spheres, each with a radius of 2 cm and a mass of 1 kg.
- The distance between the surfaces of the two spheres is 1 cm.

### Step 2: Calculate the Center-to-Center Distance
- Since each sphere has a radius of 2 cm, the center-to-center distance (d) between the two spheres is:
\[ d = \text{distance between surfaces} + \text{radius of sphere 1} + \text{radius of sphere 2} = 1 \text{ cm} + 2 \text{ cm} + 2 \text{ cm} = 5 \text{ cm} = 0.05 \text{ m} \]

### Step 3: Apply the Gravitational Force Formula
- The gravitational force (F) between two masses can be calculated using Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( G \) is the gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)), \( m_1 \) and \( m_2 \) are the masses of the spheres (1 kg each), and \( r \) is the center-to-center distance (0.05 m).

### Step 4: Substitute the Values
- Plugging in the values:
\[ F = \frac{6.67 \times 10^{-11} \cdot 1 \cdot 1}{(0.05)^2} = \frac{6.67 \times 10^{-11}}{0.0025} = 2.668 \times 10^{-8} \, \text{N} \]

### Step 5: Calculate the Acceleration
- Using Newton's second law \( F = m \cdot a \), we can find the acceleration (a) experienced by each sphere:
\[ a = \frac{F}{m} = \frac{2.668 \times 10^{-8}}{1} = 2.668 \times 10^{-8} \, \text{m/s}^2 \]

### Step 6: Analyze the Result
- The calculated acceleration \( 2.668 \times 10^{-8} \, \text{m/s}^2 \) is extremely small and negligible.
- Therefore, the gravitational attraction between the two spheres is insufficient to cause any noticeable movement.

### Conclusion
- Since the gravitational force is very weak and the acceleration is negligible, the two spheres will not move towards or away from each other significantly. Thus, the correct answer is:
**None of these.**

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