Copper of fixed volume is drawn into wire of length . When this wire is subjected to a constant force , the extension produced in the wire is . Which of the following graphs is a straight line? [2014]

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Solution

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 [2014]

1 $Δ l$ versus $1 / l$

2 $Δ l$ versus $l^{2}$

3 $Δ l$ versus $1 / l^{2}$

4 $Δ l$ versus $l$

Ans.
(2)

As $V = A l$ ...(i)

where $A$ is the area of cross-section of the wire.

Young’s modulus, $Y = \frac{(F / A)}{(Δ l / l)} = \frac{F l}{A Δ l}$

$Δ l = \frac{F l}{Y A} = \frac{F l^{2}}{Y V} (Using (i))$

$Δ l \propto l^{2}$

Hence, the graph between $Δ l$ and $l^{2}$ is a straight line.

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