Two identical balls moving in opposite direction with speed 20 m/s and 25 m/s undergo head on perfectly inelastic collision. The spped of combined mass after collision is

Options

A. `20 m/s`
B. `22.5 m/s`
C. `25 m/s`
D. `2.5 m/s`

Explanation

To solve the problem of two identical balls undergoing a perfectly inelastic collision, we will follow these steps:

### Step 1: Understand the Given Information
We have two identical balls:
- Ball 1 is moving to the right with a speed of 20 m/s.
- Ball 2 is moving to the left with a speed of 25 m/s.

### Step 2: Define the Direction
For our calculations:
- We will take the right direction as positive.
- Therefore, the velocity of Ball 1 (V1) = +20 m/s.
- The velocity of Ball 2 (V2) = -25 m/s (since it is moving in the opposite direction).

### Step 3: Write the Expression for Initial Momentum
The initial momentum (P_initial) of the system can be calculated using the formula:
\[ P_{\text{initial}} = m \cdot V_1 + m \cdot V_2 \]
Since the balls are identical, we can denote their mass as \( m \):
\[ P_{\text{initial}} = m \cdot 20 + m \cdot (-25) \]
\[ P_{\text{initial}} = 20m - 25m = -5m \]

### Step 4: Write the Expression for Final Momentum
In a perfectly inelastic collision, the two balls stick together after the collision. The final momentum (P_final) can be expressed as:
\[ P_{\text{final}} = (m + m) \cdot V \]
\[ P_{\text{final}} = 2m \cdot V \]

### Step 5: Apply the Conservation of Momentum
According to the law of conservation of momentum:
\[ P_{\text{initial}} = P_{\text{final}} \]
Substituting the expressions we derived:
\[ -5m = 2m \cdot V \]

### Step 6: Solve for V
To find the velocity \( V \):
1. Divide both sides by \( m \) (assuming \( m \neq 0 \)):
\[ -5 = 2V \]
2. Now, solve for \( V \):
\[ V = \frac{-5}{2} = -2.5 \, \text{m/s} \]

### Step 7: Interpret the Result
The negative sign indicates that the direction of the combined mass after the collision is to the left.

### Final Answer
The speed of the combined mass after the collision is **2.5 m/s to the left**.

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