(A) : An electron and proton entres a magnetic field with equal velocities, then, the force experienced by proton will be more than electron.
(R) : The charge of proton is 1837 times more than the charge of electron.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that when an electron and a proton enter a magnetic field with equal velocities, the force experienced by the proton will be more than that experienced by the electron.
- The force experienced by a charged particle moving in a magnetic field is given by the formula:
\[ F = q(v \times B) \]
- Here, \( F \) is the magnetic force, \( q \) is the charge of the particle, \( v \) is the velocity, and \( B \) is the magnetic field.

2. **Analyzing the Situation**:
- Since both the electron and proton are entering the magnetic field with equal velocities, we can denote this common velocity as \( v \).
- The charges of the electron and proton are:
- Charge of electron (\( q_e \)) = \(-1.6 \times 10^{-19}\) C
- Charge of proton (\( q_p \)) = \(+1.6 \times 10^{-19}\) C
- The magnitudes of the charges are equal, but their signs are opposite.

3. **Calculating the Forces**:
- The force experienced by the electron:
\[ F_e = q_e \cdot v \cdot B = (-1.6 \times 10^{-19}) \cdot v \cdot B \]
- The force experienced by the proton:
\[ F_p = q_p \cdot v \cdot B = (1.6 \times 10^{-19}) \cdot v \cdot B \]
- The magnitudes of the forces are equal:
\[ |F_e| = |F_p| = 1.6 \times 10^{-19} \cdot v \cdot B \]

4. **Conclusion on the Assertion**:
- Since the magnitudes of the forces experienced by both particles are equal, the assertion that the force experienced by the proton is more than that experienced by the electron is **false**.

5. **Understanding the Reason (R)**:
- The reason states that the charge of the proton is 1837 times more than the charge of the electron.
- This statement is also incorrect. The charges of the electron and proton are equal in magnitude, both being \(1.6 \times 10^{-19}\) C.
- The mass of the proton is approximately 1837 times that of the electron, not the charge.

6. **Conclusion on the Reason**:
- Since the reason provided is also false, we conclude that both the assertion and the reason are incorrect.

### Final Answer:
Both the assertion (A) and the reason (R) are false.