Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

Options

A. L = 100 cm, r = 1 mm
B. L = 200 cm, r = 3 mm
C. L = 300 cm, r = 3 mm
D. L = 400 cm, r = 4 mm

Answer

a

Explanation

`Delta L = (FL)/(AY)`
Because, wires of the same material are stretched by the same load. So, F and Y will be constant
`:. Delta L prop (L)/(pi r^(2))`
`:. Delta L_(1) = (100)/(pi xx (1 xx 10^(-3))^(2)) = (100)/(pi xx 10^(-6)) = (100)/(pi) xx 10^(-6)`
`:. Delta L_(2) = (200)/(pi xx (3 xx 10^(-3))^(2)) = (200)/(pi xx 9 xx 10^(-6)) = (22.2)/(pi) xx 10^(6)`
`:. Delta L_(3) = (300)/(pi xx (3 xx 10^(-3))^(2)) = (300)/(pi xx 9 xx 10^(-6)) = (33.3)/(pi) xx 10^(6)`
`:. Delta L_(4) = (400)/(pi xx (4 xx 10^(-3))^(2)) = (400)/(pi xx 16 xx 10^(-6)) = (25)/(pi) xx 10^(6)`
We can see that, L = 100 cm and r = 1 mm will elongate most.