In problem 9 the acceleration of the particle is

Options

A. `(10)/(pi)m` and `5pi(m)/(s^2)`
B. `(5)/(pi)m` and `(5pi)/(2)(m)/(s^2)`
C. `(10)/(pi)m` and `(5pi)/(2)(m)/(s^2)`
D. `(5)/(pi)m` and `(5pi)/(4)(m)/(s^2)`

Explanation

To solve the problem regarding the acceleration of a particle in simple harmonic motion, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Maximum displacement (amplitude), \( A = 10/\pi \) meters.
- Angular frequency, \( \omega = \frac{\pi}{2} \) radians/second.

2. **Use the Formula for Maximum Acceleration**:
The maximum acceleration \( a_{max} \) in simple harmonic motion is given by the formula:
\[ a_{max} = \omega^2 A \]

3. **Substitute the Values into the Formula**:
- First, calculate \( \omega^2 \):
\[ \omega^2 = \left(\frac{\pi}{2}\right)^2 = \frac{\pi^2}{4} \]
- Now substitute \( \omega^2 \) and \( A \) into the acceleration formula:
\[ a_{max} = \frac{\pi^2}{4} \cdot \frac{10}{\pi} \]

4. **Simplify the Expression**:
- Simplifying the expression:
\[ a_{max} = \frac{10\pi^2}{4\pi} = \frac{10\pi}{4} = \frac{5\pi}{2} \text{ m/s}^2 \]

5. **Conclusion**:
- The maximum acceleration of the particle is:
\[ a_{max} = \frac{5\pi}{2} \text{ m/s}^2 \]

### Final Answer:
The maximum acceleration of the particle is \( \frac{5\pi}{2} \text{ m/s}^2 \).

---