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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 formed? |
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Answer» Given, Diameter of metallic cylinder = 1 cm Radius of cylinder = \(\frac{1}{2}\) cm Length of cylinder = 5 cm Diameter of wire drawn from it = 1 mm = 0.1 cm Let length of wire = h cm so, Length of wire drawn from metal = \(\frac{volume\,of\,metal}{volume\,of\,wire}\) = \(\frac{π\times \frac{1}{4}\times 5}{π\times 0.1^2}\) = 500 cm = 5 m Volume of the cylinder is V = π r2 h = π 5/4 cm3 The wire is drawn into cylinder of radius 0.05cm and length L (1mm = 0.1cm = 2*radius) Therefore L π (0.05cm)2 = π 5/4 cm3 ⇒ L = 500cm |
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