Question

10. A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is
drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained ?​

Answer 1

$\huge{\bold{\sf{Given:}}}$

• $\sf\small{Diameter \:of\: metallic\: cylinder \:=\: 1\: cm}$
• $\sf\small{Radius\: of \:metallic \:cylinder \:=\:d/2\:= \:1/2}$$\sf\small{=\:0.5 \:cm}$
• $\sf\small{Length \:of \:cylinder \:=\: 5\: cm}$
• $\sf\small{Diameter \:of \:wire\: drawn \:from\: it\:=\:1\:mm}$$\sf\small{ =\:0.1\: cm}$
• $\sf\small{Radius\: of \:wire \:= \:0.5\:mm\: = \:0.05\:cm}$

$\huge{\bold{\sf{Find:}}}$

• $\sf\small{What \:will \:be\: the \:length \:of\: the}$$\sf\small{ wire\: so \:obtained \:=\:?}$

$\huge{\bold{\sf{Solution:}}}$

• $\small{\bold{\sf{Length\: of \:wire\: drawn \:from \:metal \:=}}}$$\small{\bold{\sf{volume\:of\: wire\:=\: πr²h\: / \:πr²}}}$

$\sf\small{\:\:=\:(½)² \:×\: 5\:/\:(0.05)²}$

$\sf\small{\:\:=\:(5\: / \:4) \:/\:0.0025}$

$\sf\small{\:\:=\:1.25\:/\:0.0025}$

$\sf\small{\:\:=\: 500 \:cm}$

$\sf\small{\:\:=\: 5m}$

• $\small{\underline{\underline{\boxed{\sf{∴ \:Length\: of \:the \:wire\: is \:5m.}}}}}$

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