Question

A wire 30 m long and 2mm2 cross-section is stretched by 0.49 cm when a load of 5 kg is hung from its free end. Find longitudinal strain.

Answer 1

Given,

Length of wire = 30m

Area of cross section = 2mm²

Streched by = 0.49 cm

Load = 5kg

To find,

The longitudinal strain.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Length of wire (L) = 30m

Change in lengh (∆L) = 0.49 cm = 0.0049m = 4.9 × 10⁻³ m

Now we know that,

Longitudinal strain = Change in length / Original length

= ∆L/L = 4.9×10⁻³/30 = 1.633 × 10⁻⁴

(There's no unit of this longitudinal strain because it is a ratio of two similar physical quantities.)

(The values of, area of cross section, load etc. are needed only if we need to calculate the value of longitudinal stress by the formula of, longitudinal stress = F/A)

Hence, Longitudinal strain will be 1.633 × 10⁻⁴