Question

Example 2. A uniform wire of steel of length 2.5 m and
density 8.0 gem weighs 50 g. When stretched by a force of
10 kgf, the length increases by 2 mm. Calculate Young's
modulus of steel in N/m^2​

Answer 1

QUESTION :

A uniform wire of steel of length 2.5 m and

density 8.0 gem weighs 50 g. When stretched by a force of

10 kgf, the length increases by 2 mm. Calculate Young's

modulus of steel in N/m^2

Explanation:

We know that young's modulus = stress /strain

volume of the wire = weight/density

=> Area x length = weight / density

=> area = weight/(density * length)

weight = 50 gm = 0.05 kg

density = 8 g/cm³ = 8000 kg/m³

length = 2.5 m

Hence

Area = 0.05/(8000*2.5)

= 2.5 x 10⁻⁶

Stress = force/area

= 10/2.5 x 10⁻⁶

= 4 x 10⁶

Strain = change in length/ original length

= 2 x 10⁻³ m /2.5 m

= 8 x 10⁻⁴

Hence young's modulus = stress / strain

= 4 x 10⁶/ 8 x 10⁻⁴

= 5 x 10⁹