Statement 1: If a proton and an `alpha`-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of `alpha`-particle is double than that of proton.
Statement 2: In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and inversely proprotional to the charge of particle.

Options

A. If both statement 1 and statement 2 are ture, statement 2 is the correct explanation of statement 1.
B. If both statement 1 and statement 2 are ture, statement 2 is not the correct explanation of statement 1.
C. If statement 1 is true, statement 2 is false.
D. If statement 1 is false, statement 2 is true.

Explanation

To solve the problem, we need to analyze the statements regarding the time period of revolution of a proton and an alpha particle in a uniform magnetic field.

### Step-by-Step Solution:

1. **Understanding the Motion in a Magnetic Field**:
- When a charged particle moves in a magnetic field perpendicularly, it experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path.
- The time period \( T \) of revolution of a charged particle in a magnetic field is given by the formula:
\[ T = \frac{2\pi m}{qB} \]
where \( m \) is the mass of the particle, \( q \) is the charge of the particle, and \( B \) is the magnetic field strength.

2. **Identifying the Mass and Charge of the Particles**:
- For a proton:
- Mass \( m_p = m \)
- Charge \( q_p = q \)
- For an alpha particle (which consists of 2 protons and 2 neutrons):
- Mass \( m_{\alpha} = 4m \) (approximately four times the mass of a proton)
- Charge \( q_{\alpha} = 2q \) (twice the charge of a proton)

3. **Calculating the Time Period for Each Particle**:
- Time period for the proton:
\[ T_p = \frac{2\pi m_p}{q_p B} = \frac{2\pi m}{qB} \]
- Time period for the alpha particle:
\[ T_{\alpha} = \frac{2\pi m_{\alpha}}{q_{\alpha} B} = \frac{2\pi (4m)}{(2q)B} = \frac{4\pi m}{2qB} = \frac{2\pi m}{qB} \cdot 2 = 2T_p \]

4. **Conclusion from the Calculations**:
- From the calculations, we find that the time period of the alpha particle is indeed double that of the proton:
\[ T_{\alpha} = 2T_p \]
- Therefore, Statement 1 is true.

5. **Analyzing Statement 2**:
- Statement 2 claims that the time period of revolution of a charged particle is directly proportional to its mass and inversely proportional to its charge.
- This is consistent with the formula \( T = \frac{2\pi m}{qB} \), confirming that the time period increases with mass and decreases with charge.
- Therefore, Statement 2 is also true.

6. **Final Conclusion**:
- Both statements are true, and Statement 2 correctly explains Statement 1. Thus, the answer is that both statements are correct, and Statement 2 is the correct explanation for Statement 1.