For wires of the the same material are stretched by the same load. The dimensions are given below, which of them will elongate most ?

Options

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

Answer

D

Explanation

The elongation produced in a wire is `Delta L = (4FL)/(pi D^(2)Y)`
As F and Y are same for all four wires, `:. Delta L prop (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