(A): Electric and gravitational fields are acting along same line. When proton and `alpha`-particle are projected up vertically along that line, the time of flight is less for proton.
(R ): In the given electric field acceleration of a charged particle is directly proportional to specific charge

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 true

Answer

To solve the problem, we need to analyze the statements (A) and (R) given in the question and determine their validity based on the concepts of electric and gravitational fields.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two charged particles: a proton and an alpha particle.
- Both particles are projected vertically in the presence of electric and gravitational fields acting along the same line.

2. **Identifying Forces**:
- The gravitational force acting on a particle is given by \( F_g = mg \), where \( m \) is the mass of the particle and \( g \) is the acceleration due to gravity.
- The electric force acting on a charged particle in an electric field \( E \) is given by \( F_e = qE \), where \( q \) is the charge of the particle.

3. **Net Force and Acceleration**:
- The net force acting on the particle when projected upwards is the sum of the gravitational force and the electric force:
\[ F_{net} = mg + qE \]
- The acceleration \( a \) of the particle can be expressed as:
\[ a = \frac{F_{net}}{m} = g + \frac{qE}{m} \]

4. **Time of Flight**:
- The time of flight \( T \) for a particle projected upwards with an initial velocity \( u \) can be derived from the equations of motion. The total displacement when the particle returns to the original position is zero:
\[ T = \frac{2u}{a} \]
- Substituting the expression for acceleration, we have:
\[ T = \frac{2u}{g + \frac{qE}{m}} \]

5. **Specific Charge**:
- The specific charge \( \frac{q}{m} \) is defined as the charge per unit mass of the particle.
- For a proton, \( q = e \) (charge of a proton) and \( m = m_p \) (mass of a proton).
- For an alpha particle, \( q = 2e \) (charge of an alpha particle) and \( m = 4m_p \) (mass of an alpha particle).

6. **Calculating Specific Charges**:
- For the proton:
\[ \text{Specific charge of proton} = \frac{e}{m_p} \]
- For the alpha particle:
\[ \text{Specific charge of alpha particle} = \frac{2e}{4m_p} = \frac{e}{2m_p} \]

7. **Comparing Specific Charges**:
- The specific charge of the proton is \( \frac{e}{m_p} \) which is greater than that of the alpha particle \( \frac{e}{2m_p} \).
- Since the acceleration is directly proportional to the specific charge, the proton will experience greater acceleration than the alpha particle.

8. **Conclusion on Time of Flight**:
- Since the time of flight is inversely proportional to acceleration, the proton, having a higher specific charge, will have a shorter time of flight compared to the alpha particle.

9. **Validity of Statements**:
- Statement (A) is true: The time of flight is less for the proton.
- Statement (R) is true: The acceleration of a charged particle is directly proportional to its specific charge.

### Final Answer:
Both statements (A) and (R) are true, and (R) correctly explains (A).