The length of an elastic string is 5 metre when the longitudinal tension is 4 N and 6 metre when the tension is 5 N. If the length of the string (in metre) is "2X" when the longitudinal tension is 9 N (assume Hooke’s law is valid) then the value of X will be :

Explanation

To solve the problem, we will use Hooke's law, which states that the force exerted by a spring is proportional to its extension or compression from its natural length.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the string when tension is 4 N: \( L_1 = 5 \, \text{m} \)
- Length of the string when tension is 5 N: \( L_2 = 6 \, \text{m} \)
- Length of the string when tension is 9 N: \( L = 2X \)
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