The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?

Options

A. L = 100 cm, r = 0.2 cm
B. L = 200 cm, r = 0.4 cm
C. L = 300 cm, r = 0.6 cm
D. L = 400 cm, r = 0.8 cm

Answer

a

Explanation

Extension of wire, `e = (FL)/(AY)`
`e = (FL)/(pi r^(2) Y)`
F and Y are same for all wire,
`:. E prop (L)/(r^(2))`
`e_(a) = (100)/(0.2 xx 0.2) = 2500`
and `e_(b) = (200)/(0.4 xx 0.4) = 1250`
e_(c ) = (300)/(0.6 xx 0.6) = 833.34`
and `e_(d) = (400)/(0.8 xx 0.8) = 625`
We cansee that, first wire have the largest extension