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Assertion : A particle has constant acce...

Assertion : A particle has constant acceleration is x-y plane. But neither of its acceleration components `(a_x and a_y)` is zero. Under this condition particle cannot have parabolic path.
Reason : In projectile motion, horizontal component of acceleration is zero.

A

(a)If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

(b)If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.

C

(c) If Assertion is true, but the Reason is false.

D

(d) If Assertion is false, but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-step Solution: 1. **Understanding the Assertion**: - The assertion states that a particle with constant acceleration in the x-y plane cannot have a parabolic path if neither of its acceleration components \( a_x \) and \( a_y \) is zero. - A parabolic path implies that the motion can be described by a quadratic equation in terms of displacement, which is characteristic of projectile motion. 2. **Analyzing the Conditions**: - For a particle to follow a parabolic trajectory, it must experience a constant acceleration in one direction (typically downward due to gravity) while having zero acceleration in the perpendicular direction (horizontal). - If both \( a_x \) and \( a_y \) are non-zero, the trajectory will not be purely parabolic. Instead, it will be a more complex path due to the influence of both acceleration components. 3. **Conclusion on the Assertion**: - Since the assertion claims that a particle cannot have a parabolic path if both acceleration components are non-zero, this statement is **incorrect**. A particle can indeed have a parabolic path if it has a specific configuration of acceleration components (e.g., one being zero). 4. **Understanding the Reason**: - The reason states that in projectile motion, the horizontal component of acceleration is zero. - This is true because, in ideal projectile motion, the only acceleration acting on the particle is due to gravity, which acts vertically downwards. Hence, there is no horizontal acceleration. 5. **Conclusion on the Reason**: - The reason provided is **true**. In projectile motion, the horizontal acceleration is indeed zero. 6. **Final Assessment**: - Since the assertion is false and the reason is true, the correct conclusion is that the assertion does not hold, while the reason is valid. ### Final Answer: - Assertion: False - Reason: True
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-step Solution: 1. **Understanding the Assertion**: - The assertion states that a particle with constant acceleration in the x-y plane cannot have a parabolic path if neither of its acceleration components \( a_x \) and \( a_y \) is zero. - A parabolic path implies that the motion can be described by a quadratic equation in terms of displacement, which is characteristic of projectile motion. ...
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