Introduction:
When a weight is suspended from a wire, it causes the wire to stretch or elongate due to the force applied. This phenomenon is known as the elastic deformation of the wire. The increase in length of the wire depends on various factors such as the material of the wire, its dimensions, and the magnitude of the applied force.

Given:
Length of the wire = L
Radius of the wire = r
Increase in length of the wire = 1 mm = 0.001 m

Scenario 1:
In the first scenario, a weight is suspended from a wire of length L and radius r, resulting in an increase in length of 1 mm.

Scenario 2:
In the second scenario, the same weight is suspended from a wire of double the length and double the radius of the original wire.

Analysis:
To determine the increase in length of the wire in scenario 2, we need to understand the relationship between the increase in length and the dimensions of the wire. The increase in length is directly proportional to the applied force and the original length of the wire, and inversely proportional to the cross-sectional area of the wire.

In scenario 2, the length of the wire is doubled (2L) and the radius is also doubled (2r). Let's compare the cross-sectional areas of the wires in both scenarios.

Comparison of Cross-Sectional Areas:
Cross-sectional area of the original wire (A1) = πr^2
Cross-sectional area of the wire in scenario 2 (A2) = π(2r)^2 = 4πr^2

Therefore, the cross-sectional area of the wire in scenario 2 is four times larger than the original wire.

Conclusion:
In scenario 2, the wire has a larger cross-sectional area, which means it can withstand a greater force without undergoing the same elongation. Therefore, the increase in length of the wire in scenario 2 will be less than 1 mm.

To determine the exact increase in length, we need to consider the material properties of the wire and calculate the strain using Hooke's Law. However, without additional information about the material and its properties, we can conclude that the increase in length will be less than 1 mm in scenario 2.