Assertion : In x=5-4`"sinomegat` , motion of body is SHM about the mean position x=5
Reason Amplitude of oscillation is 9.

Options

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.

Explanation

To solve the question step by step, let's analyze the assertion and reason provided.

### Step 1: Understand the Assertion
The assertion states that the equation \( x = 5 - 4 \sin(\omega t) \) describes simple harmonic motion (SHM) about the mean position \( x = 5 \).

### Step 2: Identify the Mean Position
In SHM, the mean position is where the displacement is zero. From the equation \( x = 5 - 4 \sin(\omega t) \), we can see that when \( \sin(\omega t) = 0 \), \( x \) reaches its mean position:
\[ x = 5 - 4 \cdot 0 = 5 \]
Thus, the mean position is indeed \( x = 5 \).

### Step 3: Determine the Amplitude
The amplitude of SHM is defined as the maximum displacement from the mean position. In the equation \( x = 5 - 4 \sin(\omega t) \), the term \( -4 \) indicates that the maximum displacement from the mean position (5) is 4 units. Therefore, the amplitude is:
\[ \text{Amplitude} = 4 \text{ units} \]

### Step 4: Analyze the Reason
The reason states that the amplitude of oscillation is 9 units. However, we have calculated that the amplitude is actually 4 units, not 9. Therefore, the reason is incorrect.

### Step 5: Conclusion
Based on our analysis:
- The assertion is true: The motion described is indeed SHM about the mean position \( x = 5 \).
- The reason is false: The amplitude is not 9 units; it is 4 units.

Thus, the correct answer is that the assertion is true, but the reason is false.

### Final Answer
Assertion is true, Reason is false.

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