A copper rod of diameter 2 …

A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m.We have to find the thickness of the wire.

We know that,
1 m = 1000 mm and 1 cm = 10 mm
Given Diameter of silver rod = 2 cm = 20 mm
{tex}\Rightarrow{/tex} Radius of silver rod (r₁) = 1 cm = 10 mm
Length of the silver rod (h₁) = 10 cm = 100 mm
Length of the wire (h₂) = 10 m = 10000 mm
Let the radius of the wire be r₂ cm.
As the wire is made from the rod
{tex}\Rightarrow{/tex}Volume of the rod = Volume of the wire
{tex}\Rightarrow \pi r _ { 1 } ^ { 2 } h _ { 1 } = \pi r _ { 2 } ^ { 2 } h _ { 2 }{/tex}
{tex}\Rightarrow \pi \times ( 10 ) ^ { 2 } \times 100 = \pi \times r _ { 2 } ^ { 2 } \times 10000{/tex}
{tex}\Rightarrow{/tex}10000 = {tex}r _ { 2 } ^ { 2 } \times{/tex}10000
{tex}\Rightarrow{/tex} r₂² = 1
{tex}\Rightarrow{/tex} r₂= 1 cm
Diameter of the wire (d{tex}_2{/tex}) = 2{tex}\times{/tex}1
= 2mm
Diameter of the wire (d₂) = Thickness of the wire = 2mm