A massless string passes over a frictionless pulley and carries mass `m_1` hanging at one end and mass `m_2` connected by another massless string to mass `m_3` at other end as shown in figure. Calculate the tension in string joining masses `m_2 and m_3`.

Explanation

To solve the problem of finding the tension in the string joining masses \( m_2 \) and \( m_3 \), we will analyze the forces acting on each mass and apply Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify the Forces**:
- For mass \( m_1 \) hanging, the forces are:
- Weight: \( m_1 g \) (downward)
- Tension \( T_1 \) (upward)
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