The breaking force for a wire is F. What'll be the breaking force for (a) 2 parallel wires of same size (b) a single wire of double the thickness ?

To tackle the question about the breaking force of wires, we need to understand how the properties of materials and their configurations affect their strength. Let's break it down step by step.

Understanding Breaking Force

The breaking force of a wire, denoted as F, is the maximum force that the wire can withstand before it fails or breaks. This force is influenced by the material's tensile strength and the cross-sectional area of the wire.

Scenario (a): Two Parallel Wires of the Same Size

When we have two parallel wires of the same size, each wire can carry the same breaking force, F. Since they are in parallel, the total breaking force is the sum of the breaking forces of each wire.

• Breaking force of wire 1 = F
• Breaking force of wire 2 = F

Thus, the total breaking force for the two parallel wires is:

Total Breaking Force = F + F = 2F

Scenario (b): A Single Wire of Double the Thickness

Now, let's consider a single wire that is double the thickness of the original wire. The breaking force is related to the cross-sectional area of the wire. The area of a wire is calculated using the formula for the area of a circle, A = πr², where r is the radius of the wire.

If the thickness (or diameter) of the wire is doubled, the radius also doubles. Therefore, the new area becomes:

• New radius = 2r
• New area = π(2r)² = π(4r²) = 4πr²

This means the new area is four times the original area. Since the breaking force is proportional to the cross-sectional area, the breaking force of the thicker wire will be:

New Breaking Force = 4F

Comparing the Two Scenarios

To summarize:

• For two parallel wires of the same size, the breaking force is 2F.
• For a single wire of double the thickness, the breaking force is 4F.

In conclusion, the single wire of double the thickness is stronger than the two parallel wires, as it can withstand a breaking force of 4F compared to the 2F of the two parallel wires. This illustrates how changes in dimensions can significantly impact the strength of materials.