Two wires are made of same metal. The length of the first wire is half that of the second wire and its diameter is double that of the second wire. If equal loads are applied on both wires, find the ratio of increases in their lengths.

Explanation

To solve the problem, we need to find the ratio of increases in lengths (ΔL1/ΔL2) of two wires made of the same metal, given their dimensions and the same load applied to both.

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Let the length of the second wire be \( L \).
- Therefore, the length of the first wire \( L_1 = \frac{L}{2} \).
- Let the radius of the second wire be \( R \).
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