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?

Answer 1

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 .