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Question
A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find thickness of wire?
Solution
Given diameter of copper rod(d1) = 1cm
Radius`(r_1)=1/2=0.5cm`
Length of copper rod (h1) = 8cm
Volume of cylinder`=pir_1^2h_1`
`V_1=pi(0.5)^2xx8cm^3` ........(1)
`V_2=pir_2^2h_2`
Length of wire(h2) = 18m = 1800cm
`V_2=pir_2^2(1800)cm^3` ........(2)
Equating (1) and (2)
V1 = V2
`pi(0.5)^2xx8=pir_2^2(1800)`
`(pi(0.5)^2xx8)/(pi(1800))=r_2^2`
r2 = 0.033cm
∴Radius thickness of wire = 0.033cm .
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