A particle of mass m=5g is executing simple harmonic motion with an amplitude 0.3 m and time period `(pi)/(2)` sec. The maximum value of force acting on the particle is

Options

A. 5 N
B. 4 N
C. 0.5 N
D. `0.15 ` N

Explanation

To find the maximum force acting on a particle executing simple harmonic motion (SHM), we can follow these steps:

### Step 1: Identify the given values
- Mass of the particle, \( m = 5 \, \text{g} = 0.005 \, \text{kg} \) (conversion from grams to kilograms)
- Amplitude, \( A = 0.3 \, \text{m} \)
- Time period, \( T = \frac{\pi}{2} \, \text{s} \)

### Step 2: Calculate the angular frequency (\( \omega \))
The angular frequency \( \omega \) is given by the formula:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of \( T \):
\[ \omega = \frac{2\pi}{\frac{\pi}{2}} = 4 \, \text{rad/s} \]

### Step 3: Calculate the maximum acceleration (\( a_{\text{max}} \))
The maximum acceleration in SHM is given by the formula:
\[ a_{\text{max}} = \omega^2 A \]
Substituting the values of \( \omega \) and \( A \):
\[ a_{\text{max}} = (4)^2 \times 0.3 = 16 \times 0.3 = 4.8 \, \text{m/s}^2 \]

### Step 4: Calculate the maximum force (\( F_{\text{max}} \))
The maximum force is calculated using Newton's second law:
\[ F_{\text{max}} = m \cdot a_{\text{max}} \]
Substituting the values of \( m \) and \( a_{\text{max}} \):
\[ F_{\text{max}} = 0.005 \, \text{kg} \times 4.8 \, \text{m/s}^2 = 0.000024 \, \text{N} = 0.024 \, \text{N} \]

### Final Answer
The maximum value of the force acting on the particle is:
\[ F_{\text{max}} = 0.024 \, \text{N} \]

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