Assertion : Two bodies of unequal masses `m_1 and m_2` are dropped from the same height. If the resistance offered by air to the motion of both bodies is the same, the bodies will reach the earth at the same time.
Reason : For equal air resistance, acceleration of fall of masses `m_1 and m_2` will be different.

Options

A. If the both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze the assertion and reason provided:

**Assertion:** Two bodies of unequal masses \( m_1 \) and \( m_2 \) are dropped from the same height. If the resistance offered by air to the motion of both bodies is the same, the bodies will reach the earth at the same time.

**Reason:** For equal air resistance, the acceleration of fall of masses \( m_1 \) and \( m_2 \) will be different.

### Step-by-Step Solution:

1. **Understanding Forces Acting on the Bodies:**
- When two bodies are dropped, they experience two main forces: gravitational force acting downwards and air resistance acting upwards.
- The gravitational force on body 1 is \( F_{g1} = m_1 g \) and for body 2, it is \( F_{g2} = m_2 g \).
- The air resistance force acting on both bodies is the same, denoted as \( F \).

2. **Setting Up the Equations of Motion:**
- For body 1 (mass \( m_1 \)):
\[ m_1 g - F = m_1 a_1 \quad \text{(1)} \]
- For body 2 (mass \( m_2 \)):
\[ m_2 g - F = m_2 a_2 \quad \text{(2)} \]

3. **Solving for Accelerations:**
- Rearranging equation (1):
\[ a_1 = g - \frac{F}{m_1} \]
- Rearranging equation (2):
\[ a_2 = g - \frac{F}{m_2} \]

4. **Comparing Accelerations:**
- Since \( F \) is the same for both bodies, the accelerations \( a_1 \) and \( a_2 \) depend on the masses \( m_1 \) and \( m_2 \).
- If \( m_1 \) and \( m_2 \) are different, then \( a_1 \) will not equal \( a_2 \) because the terms \( \frac{F}{m_1} \) and \( \frac{F}{m_2} \) will differ.

5. **Conclusion:**
- Since the accelerations are different, the two bodies will not reach the ground at the same time.
- Therefore, the assertion is **false** and the reason is **true**.

### Final Answer:
- The assertion is false, and the reason is true. Thus, the correct option is that the assertion is false but the reason is true.