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

Options

G1 Physics · Accepted Answer

Step 1: Hooke's law gives extension Δl = Fl/(AY). Step 2: The volume of wire is fixed: V = Al, so area A = V/l. Step 3: Substituting, Δl = Fl/[(V/l)Y] = (F/(VY))l². Step 4: F, V and Y are constants; hence Δl ∝ l². Step 5: A graph of Δl on the vertical axis versus l² on the horizontal axis is a straight line passing through the origin. Final answer: (B) Δl versus l².