Four wires of the same material are stretched by the same load. The dimensions are given below. Which one of them wil elongate the most?

Options

A. Length 100 cm, diameter 1 cm
B. Length 200 cm, diameter 2 cm
C. Length 300 cm, diameter 3 cm
D. Length 400 cm, diameter 0.5 cm

Answer

D

Explanation

The elongation produced in a wire is,
`DeltaL=(4FL)/(piD^(2)Y)`
As F and Y are same for all four wires,
`therefore" "DeltaLprop(L)/(D^2)`
For wire 1, `(L)/(D^2)=(100)/(1^2)=100`
For wire 2, `(L)/(D^2)=(200)/(2^2)=50`
For wire 3, `(L)/(D^2)=(300)/(3^2)=(100)/(3)`
For wire 4, `(L)/(D^2)=(400)/((0.5)^(2))=1600`
Thus the wire 4 will elongate the most.