Question

The filament in an incandescent light bulb is made from tungsten metal (rho = 19.3 g/cm3) that has been drawn into a very thin wire. The diameter of the wire is difficult to measure directly, so it is sometimes estimated by measuring the mass of a fixed length of wire. If a 0.200 m length of tungsten wire weighs 42.9 mg, then what is the diameter of the wire? Express your answer in millimetres.

Answer 1

Diameter of the wire is 0.119 mm.

Step-by-step explanation:

Density of the metal =
`\rho =19.3 g/cm^3`

Mas of the wire = m = 42.9 mg = 0.0429 g

1 mg = 0.001 g

Let the radius of the wire be r

Length or height of the wire = h = 0.200 m = 20 cm

1 m = 100 cm

Volume of the wire = V

`V=\pi r^2 h=3.14* r^2* 20 cm`

`\rho =(m)/(V)`

`19.3 g/cm^3=(0.0429 g)/(3.14* r^2* 20 cm)`

`r=\sqrt{(0.0429 g)/(3.14* 20 cm* 19.3 g/cm^3)}`

r = 0.00595 cm = 0.0595 mm (1 cm = 10 mm)

Diameter of the wire = d = 2r = 0.119 mm.