A body of rest mass `m_0` collides perfectly inelastically at a speed of 0.8c with another body of equal rest mass kept at rest . Calculate the common speed of the bodies after the collision and the rest mass of the combined body .

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the initial momentum before the collision
The initial momentum of the system is given by the momentum of body A (moving at 0.8c) and body B (at rest).

\[ p_{\text{initial}} = p_A + p_B = \frac{m_0}{\sqrt{1 - (0.8c)^2/c^2}} \cdot (0.8c) + 0 \]
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