Question : An iron rod with a diameter of 4 cm and length of 12 cm is drawn into a wire of length 12 m of uniform thickness. Determine the thickness of the wire.
Option 1: 0.6 cm
Option 2: 0.7 cm
Option 3: 0.3 cm
Option 4: 0.4 cm
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Correct Answer: 0.4 cm
Solution : Diameter of iron rod, $D$ = 4 cm Length of iron rod, $L$ = 12 cm Length of wire, $l$ = 12 m = 1200 cm Let $d$ be the diameter of the wire. The volume of iron rod = volume of wire ⇒ $\frac{\pi D^2 L}{4}$ = $\frac{\pi d^2 l}{4}$ ⇒ $4^2 × 12$ = $d^2 × 1200$ ⇒ $d^2$ = $4^2 × 0.01$ ⇒ $d$ = $0.4$ Hence, the correct answer is 0.4 cm.
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