Question

A copper rod of radius 1 cm and length 2 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Answer 1

Given:

Radius of copper rod, $r_1=1cm$

Length of copper rod, $l_1=2cm$

Length of wire, $l_2=18m$

To find:

Thickness of wire, $t_2$

Both the copper rod and wire are cylinders.

Volume of a cylinder of radius $r$ and length $l$ is given by: $V=\pi r^{2}l$

Volume of copper rod is equal to the volume of wire as density and mass of the material does not change.

$V_1=V_2$

$\pi r_1^2{l}_1=\pi r_2^2{l}_2$

$r_2=\sqrt{\frac{r_1^2{l}_1}{l_2}}$

$r_2=\sqrt{\frac{1^2\times 2}{18\times 100}}$

$r_2=\frac{1}{30}cm$

Thickness of the wire is equal to the diameter which is twice the radius

$t_2=2r_2=\frac{1}{15}cm$