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 will analyze the types of forces that can act between them.

### Step-by-Step Solution:

1. **Convert the Distance to Meters:**
\[ 1 \times 10^{-10} \, \text{cm} = 1 \times 10^{-12} \, \text{m} \]
(Since \(1 \, \text{cm} = 10^{-2} \, \text{m}\), we multiply by \(10^{-2}\).)

**Hint:** Always convert units to standard SI units for calculations.

2. **Identify the Types of Forces:**
- **Gravitational Force:** Exists between any two masses, including protons.
- **Electrostatic Force (Coulomb's Force):** Exists between charged particles, such as protons.
- **Nuclear Force:** Acts between nucleons (protons and neutrons) at very short distances, typically on the order of \(10^{-15} \, \text{m}\).

**Hint:** Remember the characteristics of different forces and their ranges.

3. **Determine the Applicability of Each Force:**
- The distance \(1 \times 10^{-12} \, \text{m}\) is greater than \(10^{-15} \, \text{m}\), which means the nuclear force does not apply here.
- Both the gravitational force and the electrostatic force are applicable at this distance.

**Hint:** Compare the given distance with the known ranges of the forces.

4. **Calculate the Gravitational Force:**
The gravitational force \(F_g\) between two protons can be calculated using Newton's law of gravitation:
\[ F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \(G \approx 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\) (gravitational constant)
- \(m_1 = m_2 = m_p \approx 1.67 \times 10^{-27} \, \text{kg}\) (mass of a proton)
- \(r = 1 \times 10^{-12} \, \text{m}\)

Plugging in the values:
\[ F_g = \frac{(6.674 \times 10^{-11}) \cdot (1.67 \times 10^{-27})^2}{(1 \times 10^{-12})^2} \]

**Hint:** Make sure to square the values correctly and keep track of units.

5. **Calculate the Electrostatic Force:**
The electrostatic force \(F_e\) between two protons can be calculated using Coulomb's law:
\[ F_e = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
where:
- \(k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2\) (Coulomb's constant)
- \(q_1 = q_2 = e \approx 1.6 \times 10^{-19} \, \text{C}\) (charge of a proton)
- \(r = 1 \times 10^{-12} \, \text{m}\)

Plugging in the values:
\[ F_e = \frac{(8.99 \times 10^9) \cdot (1.6 \times 10^{-19})^2}{(1 \times 10^{-12})^2} \]

**Hint:** Ensure that you use the absolute values of the charges since we are interested in the magnitude of the force.

6. **Conclusion:**
The forces acting on the two protons are the gravitational force and the electrostatic force. The nuclear force does not apply at this distance.

**Final Answer:** The forces acting on the two protons are the **Coulombic force and the gravitational force**.