Statement-1 When two particles having same charge and same de-Broglie wavelength enter in a region of uniform transverse magnetic field, they follow circular paths of equal radius
Statement-2 The radius of circular path depends on momentum and charge

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-5
B. Statement-1 is True, Statement-2, is True, Statement-2 is NOT a correct explanation for Statement-5
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To solve the question, we need to analyze both statements and verify their correctness based on the principles of physics related to charged particles moving in a magnetic field.

### Step-by-Step Solution:

1. **Understanding the Motion of Charged Particles in a Magnetic Field**:
- When a charged particle moves through a magnetic field, it experiences a magnetic force that causes it to move in a circular path. The radius of this circular path (r) can be expressed by the formula:
\[ r = \frac{mv}{qB} \]
where:
- \( m \) = mass of the particle
- \( v \) = velocity of the particle
- \( q \) = charge of the particle
- \( B \) = magnetic field strength

2. **Analyzing Statement 1**:
- Statement 1 claims that when two particles with the same charge and the same de-Broglie wavelength enter a uniform transverse magnetic field, they follow circular paths of equal radius.
- Since both particles have the same charge (\( q \)), we can assume \( q_1 = q_2 \).
- The de-Broglie wavelength (\( \lambda \)) is given by:
\[ \lambda = \frac{h}{p} \]
where \( p \) is the momentum of the particle. Since both particles have the same de-Broglie wavelength, their momenta must also be equal:
\[ p_1 = p_2 \implies mv_1 = mv_2 \]
- Therefore, the momentum \( mv \) is the same for both particles. Given that \( q \) is the same, we can conclude that:
\[ r_1 = r_2 \]
- Thus, Statement 1 is correct.

3. **Analyzing Statement 2**:
- Statement 2 states that the radius of the circular path depends on momentum and charge.
- From the formula \( r = \frac{mv}{qB} \), we see that the radius \( r \) indeed depends on both the momentum \( mv \) and the charge \( q \).
- Therefore, Statement 2 is also correct.

4. **Conclusion**:
- Both statements are true, and Statement 2 correctly explains Statement 1. Therefore, the correct option is that both statements are true, and Statement 2 is a correct explanation for Statement 1.

### Final Answer:
- **Statement 1 is true.**
- **Statement 2 is true.**
- **Statement 2 is a correct explanation for Statement 1.**

---