A particle of 0.10kg is thrown at a speed of 400m/s. Find the work done to stop this particle.

Options

A. 40J
B. 4000J
C. 8000J
D. 3J

Explanation

To solve the problem of finding the work done to stop a particle of mass 0.10 kg thrown at a speed of 400 m/s, we can use the work-energy theorem. The theorem states that the work done on an object is equal to the change in its kinetic energy.

### Step-by-Step Solution:

1. **Identify the mass and initial velocity:**
- Mass (m) = 0.10 kg
- Initial velocity (u) = 400 m/s
- Final velocity (v) = 0 m/s (since the particle is stopped)

2. **Calculate the initial kinetic energy (KE_initial):**
The formula for kinetic energy is:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.10 \, \text{kg} \times (400 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.10 \times 160000 \]
\[ KE_{\text{initial}} = 0.05 \times 160000 = 8000 \, \text{J} \]

3. **Calculate the final kinetic energy (KE_final):**
Since the particle is stopped, the final velocity is 0 m/s:
\[ KE_{\text{final}} = \frac{1}{2} m v^2 = \frac{1}{2} \times 0.10 \, \text{kg} \times (0 \, \text{m/s})^2 = 0 \, \text{J} \]

4. **Calculate the work done (W):**
According to the work-energy theorem:
\[ W = KE_{\text{final}} - KE_{\text{initial}} \]
Substituting the values:
\[ W = 0 \, \text{J} - 8000 \, \text{J} = -8000 \, \text{J} \]
The negative sign indicates that work is done against the motion of the particle to stop it.

5. **Conclusion:**
The work done to stop the particle is 8000 J.

### Final Answer:
The work done to stop the particle is **8000 Joules**.