Question

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

Answer 1

We have,

the radius of the copper rod, `R = 2/2 =1 "cm"`

the height of the copper rod , H = 10 cm and 

the height of the wire, h = 10m = 1000 cm

Let the radius of the wire be r.

As, 

Volume of the wire= Volume of the rod 

`rArr pir^2h = piR^2H`

`rArr r^2h = R^2H`

`rArr r^2 xx 1000 = 1xx10`

`rArr r^2 = 10/100`

`rArr r^2 = 1/100`

`rArr r= sqrt(1/100)`

`rArr r = 1/10`

`rArr r=0.1 "cm"`

⇒ The diameter of the wire = 2r = 2 × 0.1 = 0.2 cm

∴ The thickness of the wire = 0.2 cm

So, the thickness of the wire is 0.2 cm or 2 mm.