Question

The following wires are made of the same material. Which of these will have the largest extension, when the same tension is applied?

(a) Length = 50cm, diameter = 0.5mm

(b) Length = 100cm, diameter = 1mm

(c) Length = 200cm, diameter = 2mm

(d) Length = 300cm, diameter = 3mm

This question was addressed to me in examination.

I want to ask this question from Elastic Limit in section Thermal Properties of Matter of Engineering Physics I

Answer 1

Correct option is (a) Length = 50cm, diameter = 0.5mm

The best I can explain: ∆l=F/A  l/Y=4F/(πD^2)  l/Y

In Length = 50cm, diameter = 0.5mm, l/D^2 = 50/0.05^2 = 2×10^4 cm^-1

In Length = 100cm, diameter = 1mm, l/D^2  = 100/0.1^2 = 10^4 cm^-1

In Length = 200cm, diameter = 2mm, l/D^2  = 200/0.2^2 = 5×10^3 cm^-1

In Length = 300cm, diameter = 3mm, l/D^2  = 300/0.3^2 = 3.3×10^3 cm^-1

Hence ∆l is maximum in Length = 50cm, diameter = 0.5mm.