First slide

Hook's Law

Question

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

Easy

A

$Δ l versus 1 / l$
B

$Δ l versus l^{2}$
C

$Δ l versus 1 / l^{2}$
D

$Δ l versus l$

Solution

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