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A: In SHM the change in velocity is not ...

A: In SHM the change in velocity is not uniform.
R: In SHM the acceleration of body varies linearly with its displacement.

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 statements, then mark (4)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion (A) and the reason (R) provided: **Assertion (A):** In SHM, the change in velocity is not uniform. **Reason (R):** In SHM, the acceleration of the body varies linearly with its displacement. ### Step-by-Step Solution: 1. **Understanding Simple Harmonic Motion (SHM):** - SHM is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the mean position and acts in the opposite direction. 2. **Analyzing the Assertion (A):** - In SHM, the velocity of the oscillating body changes as it moves through its path. The velocity is maximum at the mean position and zero at the extreme positions. - Since the velocity changes continuously and is not constant throughout the motion, we can conclude that the change in velocity is indeed not uniform. 3. **Analyzing the Reason (R):** - The acceleration in SHM is given by the formula: \[ a = -\omega^2 x \] where \( \omega \) is the angular frequency and \( x \) is the displacement from the mean position. - This equation shows that acceleration is directly proportional to the displacement \( x \) but in the opposite direction (hence the negative sign). - Therefore, as the displacement increases or decreases, the acceleration also changes linearly with it. 4. **Conclusion:** - Both the assertion (A) and the reason (R) are true. - Furthermore, the reason (R) correctly explains the assertion (A) because the non-uniform change in velocity is a result of the linear relationship between acceleration and displacement in SHM. ### Final Answer: Both the assertion and reason are true, and the reason is the correct explanation of the assertion.
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