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

Options

A. length`=50cm`,`diameter`=0.5mm`
B. length`=100cm`, diameter`=1mm`
C. length`=200cm` diameter`=2mm`
D. length`=300cm`, diameter`=3mm`

Answer

A

Explanation

`triangle_1prop(100)/(1^2)prop100`
`triangleL_2prop(100)/(2^2)prop50`
`triangleL_3prop(300)/(3^2)prop(100)/(3)`
`triangleL_3prop(50)/((1)/(4))prop200`
`triangleLprop(L)/(A)` or `triangleLprop(L)/(D^2)`
The ratio of `(L)/(D^2)` is maximum for case (a) Hence, option (a) is correct.