A ball weighing 4 kg and moving with velocity of 8 m/sec. Collides with a stationary ball of mass 12 kg. After the collision, the two balls move together. The final velocity is

Options

A. 0
B. 2 m/sec
C. 8 m/sec
D. 16 m/sec

Answer

To solve the problem step by step, we will use the principle of conservation of momentum.

### Step 1: Identify the given data
- Mass of the first ball (m1) = 4 kg
- Initial velocity of the first ball (u1) = 8 m/s
- Mass of the second ball (m2) = 12 kg
- Initial velocity of the second ball (u2) = 0 m/s (since it is stationary)

### Step 2: Write the formula for conservation of momentum
According to the law of conservation of momentum:
\[ \text{Initial Momentum} = \text{Final Momentum} \]

### Step 3: Calculate the initial momentum
The initial momentum (p_initial) can be calculated as:
\[ p_{\text{initial}} = m_1 \cdot u_1 + m_2 \cdot u_2 \]
Substituting the values:
\[ p_{\text{initial}} = (4 \, \text{kg} \cdot 8 \, \text{m/s}) + (12 \, \text{kg} \cdot 0 \, \text{m/s}) \]
\[ p_{\text{initial}} = 32 \, \text{kg m/s} + 0 \]
\[ p_{\text{initial}} = 32 \, \text{kg m/s} \]

### Step 4: Calculate the final momentum
After the collision, both balls stick together and move with a common velocity (v). The total mass after the collision is:
\[ m_{\text{total}} = m_1 + m_2 = 4 \, \text{kg} + 12 \, \text{kg} = 16 \, \text{kg} \]
The final momentum (p_final) can be expressed as:
\[ p_{\text{final}} = m_{\text{total}} \cdot v \]
So,
\[ p_{\text{final}} = 16 \, \text{kg} \cdot v \]

### Step 5: Set initial momentum equal to final momentum
Using the conservation of momentum:
\[ p_{\text{initial}} = p_{\text{final}} \]
\[ 32 \, \text{kg m/s} = 16 \, \text{kg} \cdot v \]

### Step 6: Solve for the final velocity (v)
To find v, we rearrange the equation:
\[ v = \frac{32 \, \text{kg m/s}}{16 \, \text{kg}} \]
\[ v = 2 \, \text{m/s} \]

### Conclusion
The final velocity of the two balls moving together after the collision is **2 m/s**.

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