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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