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A : In the presence of air resistance, i...

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.

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).

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reasoning provided: **Assertion (A):** In the presence of air resistance, if the ball is thrown vertically upwards, then the time of ascent is less than the time of descent. **Reason (R):** Force due to air friction always acts opposite to the motion of the body. ### Step-by-Step Solution: 1. **Understanding the Motion of the Ball:** - When a ball is thrown vertically upwards, it moves against the force of gravity (g) and also experiences air resistance (drag force). - During the ascent, both the gravitational force and the drag force act downward. 2. **Analyzing Forces During Ascent:** - The net force acting on the ball during ascent is: \[ F_{\text{net, ascent}} = -mg - F_{\text{drag}} \] - This results in a greater effective acceleration acting downwards, which means the ball will decelerate more quickly than it would without air resistance. 3. **Understanding Time of Ascent:** - Because the ball experiences a greater effective downward acceleration, it will take less time to reach its maximum height compared to a scenario without air resistance. 4. **Analyzing Forces During Descent:** - When the ball starts descending, the forces acting on it are gravity (downward) and air resistance (upward). - The net force during descent is: \[ F_{\text{net, descent}} = mg - F_{\text{drag}} \] - Here, the effective acceleration downward is reduced due to the opposing drag force. 5. **Understanding Time of Descent:** - Since the effective acceleration during descent is less than during ascent, the ball will take more time to fall back to the ground. 6. **Conclusion:** - Therefore, the assertion that the time of ascent is less than the time of descent is correct. - The reason provided is also valid as it explains why the forces act in opposite directions during ascent and descent. ### Final Answer: Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion.
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Frictional force always acts in a direction opposite to the weight of the body.

In the following problems the air resistance is constant (air resistance always opposes the motion). (a) A ball is thrown vertically upward. If time of ascent is t_(1) and time of descent is t_(2) , which time is greater ? (b) A ball is thrown vertically upward with speed u and on returning to the ground, its speed is v_(0) . Which speed is greater ? (c) Two balls A and B (m_(A) gt m_(B)) are thrown vertically upward with same speed. Which ball A or B (heavier or lighter) wil attain greater height ?

Knowledge Check

  • A ball is thrown vertically upwards .Assuming the air resistance to be constant and considerable :

    A
    the time of ascent `lt` the time of descent
    B
    the time of ascent the tine of descent
    C
    the time of ascent = the time of descent
    D
    the time of ascent `gt` the time of descent
  • A ball is thrown vertically upwards from the ground. Work done by air resistance during its time of flight is

    A
    positive during ascent and negative during descent
    B
    positive during ascent and descent
    C
    negative during ascent and positive during descent
    D
    negative during ascent and descent
  • A ball is thrown vertically with some velocity . A constant air resistance acts. If the time of ascent is t_(1) and that of descent is t_(2) , then

    A
    `t_(1) lt t_(2)`
    B
    `t_(1) gt t_(2)`
    C
    `t_(1) = t_(2)`
    D
    None
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