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Assertion : A particle performing SHM at...

Assertion : A particle performing SHM at certain instant is having velocity v. It again acquire a velocity v for the first time after a time interval of T second. Then the time period of oscillation is T second.
Reason : A particle performing SHM can have same velocity at two instants in one cycle.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we will analyze both the assertion and the reason step by step. ### Step 1: Understanding the Assertion The assertion states that if a particle performing Simple Harmonic Motion (SHM) has a velocity \( v \) at a certain instant and acquires the same velocity \( v \) again after a time interval of \( T \) seconds, then the time period of oscillation is \( T \) seconds. **Analysis**: In SHM, the particle can have the same velocity at different points in its motion. However, the time taken to return to the same velocity does not necessarily imply that this time is equal to the time period of the oscillation. The time period \( T \) is the time taken to complete one full cycle of motion, which includes moving from one extreme position to the other and back. ### Step 2: Understanding the Reason The reason states that a particle performing SHM can have the same velocity at two different instants in one cycle. **Analysis**: This statement is true. In SHM, the velocity of the particle varies sinusoidally. For example, when the particle moves from the mean position to one extreme, it has a certain velocity, and when it moves back towards the mean position from the other extreme, it can have the same magnitude of velocity at different points in its path. ### Step 3: Conclusion Based on the analysis: - The assertion is **false** because having the same velocity at two different times does not imply that the time period is equal to that time interval. - The reason is **true** because it accurately describes the nature of velocity in SHM. Thus, the correct answer is that the assertion is false and the reason is true. ### Final Answer Assertion: False Reason: True
To solve the assertion and reason question, we will analyze both the assertion and the reason step by step. ### Step 1: Understanding the Assertion The assertion states that if a particle performing Simple Harmonic Motion (SHM) has a velocity \( v \) at a certain instant and acquires the same velocity \( v \) again after a time interval of \( T \) seconds, then the time period of oscillation is \( T \) seconds. **Analysis**: In SHM, the particle can have the same velocity at different points in its motion. However, the time taken to return to the same velocity does not necessarily imply that this time is equal to the time period of the oscillation. The time period \( T \) is the time taken to complete one full cycle of motion, which includes moving from one extreme position to the other and back. ...
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