A wire can be broken by applying a load of 20 kg wt. The force required to break the wire of tw

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A wire can be broken by applying a load of 20 kg wt. The...

A wire can be broken by applying a load of $20 \mathrm{~kg}$ wt. The force required to break the wire of twice the diameter is
(a) $20 \mathrm{~kg} \mathrm{wt}$
(b) $5 \mathrm{~kg} \mathrm{wt}$
(c) $80 \mathrm{~kg} \mathrm{wt}$
(d) $160 \mathrm{~kg}$ wt

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Key Concepts

Cross-sectional Area

The cross-sectional area of a wire, particularly when it is circular, is proportional to the square of its diameter (A = ?*(d/2)^2). When the diameter is doubled, the area increases by a factor of four, which directly affects the strength of the wire because more material is available to resist the applied load.

Tensile Strength

Tensile strength refers to the maximum stress a material can withstand while being stretched or pulled before failing. It is directly related to the cross-sectional area of the material, with the breaking load increasing as the area increases. This concept is crucial when comparing wires of different diameters made from the same material.

Scaling Laws in Material Properties

Scaling laws describe how geometric changes affect physical properties. In the context of wire strength, the fact that the area scales with the square of the diameter means that a wire with twice the diameter has four times the cross-sectional area. Consequently, assuming the material’s inherent properties remain the same, the force required to break the thicker wire is also multiplied by four.

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