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Question
A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire.
Solution
We have,
the radius of the copper rod, `R = 2/2 =1 "cm"`
the height of the copper rod , H = 10 cm and
the height of the wire, h = 10m = 1000 cm
Let the radius of the wire be r.
As,
Volume of the wire= Volume of the rod
`rArr pir^2h = piR^2H`
`rArr r^2h = R^2H`
`rArr r^2 xx 1000 = 1xx10`
`rArr r^2 = 10/100`
`rArr r^2 = 1/100`
`rArr r= sqrt(1/100)`
`rArr r = 1/10`
`rArr r=0.1 "cm"`
⇒ The diameter of the wire = 2r = 2 × 0.1 = 0.2 cm
∴ The thickness of the wire = 0.2 cm
So, the thickness of the wire is 0.2 cm or 2 mm.
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