Copper of fixed volume `V` is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is `trianglel`. Which of the following graphs is a straight line?

Options

A. `Delta l` versus `(1)/(l)`
B. `Delta l` versus `l^(2)`
C. `Delta l` versus `(1)/(l^(2))`
D. `Delta l` versus `l`

Answer

b

Explanation

Young's modulus is given by
`Y = (F xx l)/(A xx Delta l)` ...(i)
As `V = A xx l` = constant ...(ii)
From Eqs. (i) and (ii), we get
`Y = (F xx l^(2))/(V xx Delta l) rArr Delta l = (F)/(V xx Y) xx l^(2)`
`rArr Delta l prop l^(2)`