These questions consists of two statements each printed as Assertion and Reason. While answering these question you are required to choose any one of the following four responses
Assertion A particle is thrown vertically upwards. If air resistance is taken into consideration then retardation in upward journey is more than the acceleration in downward journey.
Reason Some mechanical energy is lost in the form of heat due to air friction.

Options

A. If both Assertion and reason are true and the reason is a correct explanation of the assertion.
B. If both Assertion and reason are true and the reason is not the correct explanation of the assertion.
C. if assertion is true but reason is false
D. if assertion is false but reason is true

Explanation

To solve the problem, we need to analyze the assertion and reason provided and determine their validity.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when a particle is thrown vertically upwards, the retardation (deceleration) during the upward journey is greater than the acceleration during the downward journey when air resistance is considered.

2. **Analyzing the Upward Motion**:
- When the particle is thrown upwards, it experiences two forces acting against its motion:
- The force of gravity (mg) acting downwards.
- The force of air resistance (W) also acting downwards.
- The net force (F_net) acting on the particle during the upward motion is:
\[ F_{\text{net}} = W + mg \]
- The acceleration (A_u) during the upward journey can be expressed as:
\[ A_u = \frac{F_{\text{net}}}{m} = \frac{W + mg}{m} = \frac{W}{m} + g \]
- This indicates that the upward acceleration is influenced by both the gravitational force and the air resistance.

3. **Analyzing the Downward Motion**:
- During the downward journey, the forces acting on the particle are:
- The gravitational force (mg) acting downwards.
- The air resistance (W) acting upwards.
- The net force (F_net) during the downward motion is:
\[ F_{\text{net}} = mg - W \]
- The acceleration (A_d) during the downward journey can be expressed as:
\[ A_d = \frac{F_{\text{net}}}{m} = \frac{mg - W}{m} = g - \frac{W}{m} \]
- This shows that the downward acceleration is reduced by the air resistance.

4. **Comparing the Accelerations**:
- From the expressions derived:
- Upward acceleration: \( A_u = \frac{W}{m} + g \)
- Downward acceleration: \( A_d = g - \frac{W}{m} \)
- Since \( \frac{W}{m} \) is a positive value (air resistance), it follows that:
\[ A_u > A_d \]
- Therefore, the assertion that the retardation in the upward journey is greater than the acceleration in the downward journey is true.

5. **Understanding the Reason**:
- The reason states that some mechanical energy is lost in the form of heat due to air friction.
- This is true because air resistance does convert some of the mechanical energy of the particle into thermal energy, resulting in a loss of mechanical energy.

6. **Conclusion**:
- Both the assertion and the reason are true.
- The reason correctly explains the assertion since the loss of mechanical energy due to air friction contributes to the difference in retardation and acceleration.

### Final Answer:
Both Assertion and Reason are true, and the Reason is the correct explanation of the Assertion.