A : In the presence of air resistance, if the ball is thrown vertically upwards then time of ascent is less than the time of descent.
R : Force due to air friction always acts opposite to the motion of the body.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statement, then mark (4).

Answer

To solve the question regarding the assertion and reason related to the motion of a ball thrown vertically upwards in the presence of air resistance, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that in the presence of air resistance, if a ball is thrown vertically upwards, the time of ascent is less than the time of descent.
- This means that the ball will take a shorter time to reach its highest point compared to the time it takes to return to the ground.

2. **Analyzing the Forces**:
- When the ball is thrown upwards, two forces act on it: the gravitational force (downwards) and the air resistance (also acting downwards since the ball is moving upwards).
- The net force acting on the ball during its ascent is the gravitational force plus the force of air resistance.

3. **Acceleration During Ascent**:
- The total effective acceleration during ascent can be expressed as:
\[ a_{\text{up}} = g + a_{\text{air}} \]
- Here, \( g \) is the acceleration due to gravity, and \( a_{\text{air}} \) is the acceleration due to air resistance. Both act downwards, which means the ball experiences a greater deceleration.

4. **Acceleration During Descent**:
- When the ball descends, the gravitational force still acts downwards, but the air resistance acts upwards (opposite to the direction of motion).
- The effective acceleration during descent can be expressed as:
\[ a_{\text{down}} = g - a_{\text{air}} \]
- Here, the ball experiences less deceleration because the air resistance reduces the effective acceleration.

5. **Comparing Times of Ascent and Descent**:
- Since the ball experiences greater deceleration during ascent (due to both gravity and air resistance acting downwards), it takes less time to reach the highest point.
- Conversely, during descent, the ball experiences less deceleration, which means it takes more time to return to the ground.

6. **Conclusion on Assertion**:
- Therefore, the assertion is true: the time of ascent is indeed less than the time of descent when air resistance is considered.

7. **Understanding the Reason**:
- The reason states that the force due to air friction always acts opposite to the motion of the body.
- This is also true, as air resistance opposes the motion of the ball, whether it is moving upwards or downwards.

8. **Correctness of Reason as Explanation**:
- The reason correctly explains why the assertion is true. The change in the direction of the net acceleration due to air resistance affects the time taken for ascent and descent.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion. Thus, the correct option is **Option 1**.

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