A mass of 20 kg moving with a speed of 10 m / s collides with another stationary mass of . 5kg As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be

Options

A. 600 Joule
B. 800 joule
C. 1000 joule
D. 1200 joule

Answer

To solve the problem, we need to find the kinetic energy of the composite mass after the collision. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Identify the masses and their initial velocities:**
- Mass \( m_1 = 20 \, \text{kg} \) (moving with a speed of \( v_1 = 10 \, \text{m/s} \))
- Mass \( m_2 = 5 \, \text{kg} \) (stationary, so \( v_2 = 0 \, \text{m/s} \))

2. **Calculate the initial momentum of the system:**
- The total initial momentum \( p_{\text{initial}} \) can be calculated using the formula:
\[ p_{\text{initial}} = m_1 v_1 + m_2 v_2 \]
- Substituting the values:
\[ p_{\text{initial}} = (20 \, \text{kg} \times 10 \, \text{m/s}) + (5 \, \text{kg} \times 0 \, \text{m/s}) = 200 \, \text{kg m/s} \]

3. **Calculate the total mass after the collision:**
- The total mass \( m_{\text{total}} \) after the collision is:
\[ m_{\text{total}} = m_1 + m_2 = 20 \, \text{kg} + 5 \, \text{kg} = 25 \, \text{kg} \]

4. **Use conservation of momentum to find the final velocity \( v_f \) of the composite mass:**
- According to the conservation of momentum:
\[ p_{\text{initial}} = p_{\text{final}} \]
- Therefore,
\[ m_{\text{total}} v_f = p_{\text{initial}} \]
- Rearranging to find \( v_f \):
\[ v_f = \frac{p_{\text{initial}}}{m_{\text{total}}} = \frac{200 \, \text{kg m/s}}{25 \, \text{kg}} = 8 \, \text{m/s} \]

5. **Calculate the kinetic energy of the composite mass:**
- The kinetic energy \( KE \) of the composite mass can be calculated using the formula:
\[ KE = \frac{1}{2} m_{\text{total}} v_f^2 \]
- Substituting the values:
\[ KE = \frac{1}{2} \times 25 \, \text{kg} \times (8 \, \text{m/s})^2 = \frac{1}{2} \times 25 \times 64 = 800 \, \text{J} \]

### Final Answer:
The kinetic energy of the composite mass after the collision is **800 Joules**.