A particle of mass 10g is undergoing SHM of amplitude 10cm and period 0.1s. The maximum value of force on particle is about

Options

A. 5.6N
B. 2.75 N
C. 3.5 N
D. 4N

Answer

To find the maximum value of force on a particle undergoing Simple Harmonic Motion (SHM), we can follow these steps:

### Step 1: Identify the Given Values
- Mass of the particle (m) = 10 g = 0.01 kg (since 1 g = 0.001 kg)
- Amplitude (A) = 10 cm = 0.1 m (since 1 cm = 0.01 m)
- Time period (T) = 0.1 s

### Step 2: Calculate Angular Frequency (ω)
The angular frequency (ω) is given by the formula:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of T:
\[ \omega = \frac{2\pi}{0.1} = 20\pi \, \text{rad/s} \]

### Step 3: Calculate Maximum Acceleration (A_max)
The maximum acceleration in SHM is given by:
\[ A_{\text{max}} = \omega^2 \cdot A \]
Substituting the values of ω and A:
\[ A_{\text{max}} = (20\pi)^2 \cdot 0.1 \]
Calculating \( (20\pi)^2 \):
\[ (20\pi)^2 = 400\pi^2 \]
Thus,
\[ A_{\text{max}} = 400\pi^2 \cdot 0.1 = 40\pi^2 \, \text{m/s}^2 \]

### Step 4: Calculate Maximum Force (F_max)
The maximum force can be calculated using Newton's second law:
\[ F_{\text{max}} = m \cdot A_{\text{max}} \]
Substituting the values of m and \( A_{\text{max}} \):
\[ F_{\text{max}} = 0.01 \cdot 40\pi^2 \]
Calculating \( 40\pi^2 \):
\[ F_{\text{max}} = 0.01 \cdot 40 \cdot 9.87 \approx 0.01 \cdot 395.2 \approx 3.952 \, \text{N} \]

### Step 5: Approximate the Result
Rounding \( 3.952 \, \text{N} \) to the nearest whole number gives approximately:
\[ F_{\text{max}} \approx 4 \, \text{N} \]

### Final Answer
The maximum value of force on the particle is approximately **4 N**.

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