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 Δ l . Which of the following graphs is a straight line?

Question

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 Δ l . Which of the following graphs is a straight line? (A) Δ l versus 1/l (B) Δ l versus l2 (C) Δ l versus 1/l2 (D) Δ l versus l

Tardigrade Admin · Accepted Answer

As V = Al

...............(i)
where A is the area of cross-section of the wire.
Young's modulus,

Y = \frac{F / A}{Δ l / l} = \frac{Fl}{a Δ l}

Δ l = \frac{Fl}{Y A} = \frac{F l ^{2}}{YV}

(Using (i))

Δ l \propto l^{2}

Hence, the graph between

Δ l an d l^{2}

is a straight line.

Q. 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 $Δ l$ . Which of the following graphs is a straight line?

$Δ l v ers u s 1/ l$

$Δ l v ers u s l^{2}$

$Δ l v ers u s 1/ l^{2}$

$Δ l v ers u s l$

As V = Al ...............(i)
where A is the area of cross-section of the wire.
Young's modulus, $Y = \frac{F / A}{Δ l / l} = \frac{Fl}{a Δ l}$
$Δ l = \frac{Fl}{Y A} = \frac{F l ^{2}}{YV}$ (Using (i))
$Δ l \propto l^{2}$
Hence, the graph between $Δ l an d l^{2}$ is a straight line.

Q. 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 Δl. Which of the following graphs is a straight line?

Δlversus1/l

Δlversusl2

Δlversus1/l2

Δlversusl