A body of mass 5 kg moving with a velocity 10 m/s collides with another body of the mass 20 kg at, rest and comes to rest. The velocity of the second body due to collision is

Options

A. 2.5 m/s
B. 5m/s
C. 7.5 m/s
D. 10 m/s

Answer

To solve the problem, we will use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

### Step-by-Step Solution:

1. **Identify the masses and velocities:**
- Mass of the first body (m1) = 5 kg
- Initial velocity of the first body (u1) = 10 m/s
- Mass of the second body (m2) = 20 kg
- Initial velocity of the second body (u2) = 0 m/s (since it is at rest)

2. **Calculate the initial momentum:**
The total initial momentum (p_initial) can be calculated using the formula:
\[ p_{\text{initial}} = m_1 \cdot u_1 + m_2 \cdot u_2 \]
Substituting the values:
\[ p_{\text{initial}} = (5 \, \text{kg} \cdot 10 \, \text{m/s}) + (20 \, \text{kg} \cdot 0 \, \text{m/s}) = 50 \, \text{kg m/s} \]

3. **Final conditions after the collision:**
After the collision, the first body comes to rest, so its final velocity (v1) = 0 m/s. Let the final velocity of the second body (v2) be what we need to find.

4. **Calculate the final momentum:**
The total final momentum (p_final) can be calculated using the formula:
\[ p_{\text{final}} = m_1 \cdot v_1 + m_2 \cdot v_2 \]
Substituting the known values:
\[ p_{\text{final}} = (5 \, \text{kg} \cdot 0 \, \text{m/s}) + (20 \, \text{kg} \cdot v_2) = 20 \, \text{kg} \cdot v_2 \]

5. **Apply the conservation of momentum:**
According to the conservation of momentum:
\[ p_{\text{initial}} = p_{\text{final}} \]
Therefore:
\[ 50 \, \text{kg m/s} = 20 \, \text{kg} \cdot v_2 \]

6. **Solve for v2:**
Rearranging the equation to find v2:
\[ v_2 = \frac{50 \, \text{kg m/s}}{20 \, \text{kg}} = 2.5 \, \text{m/s} \]

### Final Answer:
The velocity of the second body due to the collision is **2.5 m/s**.