Question

Two wires have the same material and have the same volume. However wire 1 had cross sectional area A and wire 2 has cross sectional area 3A. If the length of wire 1 increases by ∆x on applying force F, how much force is needed to stretch wire 2 by the same amount?

(a) F

(b) 4F

(c) 6F

(d) 9F

This question was posed to me in a job interview.

Query is from Stress and Strain topic in chapter Thermal Properties of Matter of Engineering Physics I

Answer 1

Right choice is (d) 9F

Best explanation: Y=F/A  l/∆l=F/A^2   Al/∆x=FV/(A^2 ∆x)

F=Y∆x/V A^2

FαA^2

F^‘=(3A)^2

F^‘/F=9

F^‘=9F.