The resistance of a wire depends on its length, cross-sectional area, and resistivity of the material. In this question, a wire of resistance 9 ohms is broken into two parts with a length ratio of 1:2. These two wires are then connected in parallel.

Calculating the resistance of the wires:
Let's assume the resistance of the first wire is R1 and the length of the first wire is L1. Similarly, let's assume the resistance of the second wire is R2 and the length of the second wire is L2.

According to the question, the length ratio is 1:2. So, we can say that L1/L2 = 1/2.

Now, the resistance of a wire is directly proportional to its length. Therefore, we can write R1/R2 = L1/L2.

Given that R1 = 9 ohms, we can substitute these values into the equation:
9/R2 = 1/2

Cross-multiplying, we get:
2R2 = 9
R2 = 9/2
R2 = 4.5 ohms

Now, we can calculate the value of R1 using the equation:
9/R2 = L1/L2

Substituting the values, we get:
9/4.5 = L1/L2
2 = L1/L2

Since L1/L2 = 1/2, we can conclude that L1 = L2/2.

Calculating the net resistance:
When two resistors are connected in parallel, the net resistance is given by the formula:

1/Rnet = 1/R1 + 1/R2

Substituting the values, we get:
1/Rnet = 1/9 + 1/4.5
1/Rnet = 2/9

Cross-multiplying, we get:
Rnet = 9/2
Rnet = 4.5 ohms

Therefore, the net resistance of the two wires connected in parallel is 4.5 ohms.