Question

A wire of length 10 m and diameter 2 mm elongates 0.2 mm when stretched by a weight of
0.55 Kg . Calculate the youngs modulus of the material of the wire .given that g is 9.8 m per s.

Answer 1

We know that Young's modulas = stress / strain

Now,

stress = force/area

         = mg/πr²

where , m =0.55 kg

g = 9.8

r = 2/2 = 1 mm = 1 x 10⁻³ m

Hence ,

stress = 0.55x9.8 / 3.14 x 10⁻⁶

= 1.716 x 10⁶

Now strain is defined as the the ratio of change in length to original length,

strain = 0.2 x 10⁻³/10

= 0.2 x 10⁻⁴

Therefore Young's modulas = stress/strain

= 1.716 x 10⁶/ 0.2 x 10⁻⁴

= 8.58 x 10¹⁰