Three balls of masses `m_(1), m_(2)` and `m_(3)` are lying in a straight line. The first ball is moved with a certain velocity so that it strikes the second ball directly and itself comes to rest. The second ball collides with the third and is itself reduced to rest. If `e` is the coefficient of restitution for each ball, write down the relation of `m_(3)` in terms of `m_(1)` and `m_(2)`.

Explanation

To solve the problem, we will analyze the collisions step by step, applying the principles of conservation of momentum and the coefficient of restitution.

### Step 1: Understand the scenario
We have three balls with masses \( m_1 \), \( m_2 \), and \( m_3 \). The first ball \( m_1 \) moves with a certain velocity \( v \) and strikes the second ball \( m_2 \), which comes to rest after the collision. The second ball then collides with the third ball \( m_3 \) and also comes to rest.

### Step 2: Analyze the first collision
When ball \( m_1 \) collides with ball \( m_2 \):
- Before the collision:
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