Question : A cylindrical metallic rod of diameter 2 cm and length 45 cm is melted and converted into wire of uniform thickness and length 5 m. The diameter of the wire is:
Option 1: 3 mm
Option 2: 2 mm
Option 3: 6 mm
Option 4: 5 mm
Correct Answer: 6 mm
Solution : Given, A cylindrical metallic rod of diameter 2 cm and length 45 cm is melted and converted into wire of uniform thickness and length 5 m. Let $V_1$ and $V_2$ be the volumes of the cylindrical rods in the two cases. According to the question, $V_1=V_2$ We know the volume of cylinder = $\pi r^2h$, where r is the radius and h is the height ⇒ $\pi r_1^2h_1=\pi r_2^2h_2$ ⇒ $ r_1^2h_1=r_2^2h_2$ ⇒ $(10)^2\times 450=r_2^2\times 5000$ [As 5 m = 5000 mm and 1 cm = 10 mm] ⇒ $r_2^2=\frac{450\times 10\times 10}{5000}$ ⇒ $r_2^2=9$ ⇒ $r_2=3$ mm ⇒ diameter = 3 × 2 = 6 mm Hence, the correct answer is 6 mm.
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