Question

An iron rod of 1 cm diameter and 8 cm length is drawn into a wire of 18 m length of uniform thickness. calculate the thickness of the wire?

Answer 1

$\bigstar{\pmb{\huge{\underline{\mathfrak{\red{Answer}}}}}}$

For the copper rod : R = $\sf{\frac{1}{2}cm,H=8cm}$

For the copper wire : r = ?, h = 18m = 1800cm

Volume of copper wire = Volume of copper rod

= $\sf{\pi {r}^{2} \times 1800 = \pi \times \frac{1}{2} \times \frac{1}{2} \times 8}$

= $\sf{{r}^{2} = \frac{1}{900} = {( \frac{1}{30} )}^{2}}$

$\therefore$ $\sf{r = \frac{1}{30} cm}$

Hence, the diameter of cross - section or thickness of the wire

= $\sf{\frac{1}{15}cm=\frac{1}{15}×10mm}$

= $\sf{0.67mm(approx.)}$