Two protons are a distance of `1 xx 10^(-10) cm` from each other. The force acting on them are

Options

A. nuclear force and gravitational force
B. nuclear force and coulomb force
C. coulomb force and gravitational force
D. nuclear, coulomb and gravitational force

Answer

To solve the problem of determining the forces acting on two protons that are a distance of \(1 \times 10^{-10} \, \text{cm}\) apart, we can follow these steps:

### Step 1: Convert the Distance
First, we need to convert the distance from centimeters to meters for consistency in SI units.

\[ 1 \, \text{cm} = 10^{-2} \, \text{m} \]
\[ 1 \times 10^{-10} \, \text{cm} = 1 \times 10^{-10} \times 10^{-2} \, \text{m} = 1 \times 10^{-12} \, \text{m} \]

### Step 2: Identify the Forces Acting on Protons
Next, we identify the types of forces acting on the protons. The two main forces to consider are:
1. **Coulomb's Force (Electrostatic Force)**: This force arises due to the electric charge of the protons.
2. **Gravitational Force**: This force arises due to the mass of the protons.

### Step 3: Determine the Relevance of Each Force
- **Coulomb's Force**: The formula for the electrostatic force between two charges is given by Coulomb's Law:

\[ F_e = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]

Where:
- \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\)),
- \(q_1\) and \(q_2\) are the charges of the protons (\(1.6 \times 10^{-19} \, \text{C}\)),
- \(r\) is the distance between the charges (\(1 \times 10^{-12} \, \text{m}\)).

- **Gravitational Force**: The gravitational force can be calculated using Newton's law of gravitation:

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

Where:
- \(G\) is the gravitational constant (\(6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\)),
- \(m_1\) and \(m_2\) are the masses of the protons (\(1.67 \times 10^{-27} \, \text{kg}\)),
- \(r\) is the distance between the masses (\(1 \times 10^{-12} \, \text{m}\)).

### Step 4: Evaluate the Nuclear Force
The nuclear force operates at very short ranges, typically on the order of \(10^{-15} \, \text{m}\). Since the distance between the protons is \(1 \times 10^{-12} \, \text{m}\), which is greater than \(10^{-15} \, \text{m}\), the nuclear force does not play a significant role in this scenario.

### Step 5: Conclusion
Based on the analysis:
- The forces acting on the protons are the **Coulomb's force (electrostatic force)** and the **gravitational force**.
- The nuclear force is negligible at this distance.

Thus, the correct answer is that the forces acting on the protons are **Coulomb's force and gravitational force**.

### Final Answer
The forces acting on the two protons are **Coulomb's force and gravitational force**.

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