Question

A wire gets stretched by 4mm due to a certain load. If the same load is applied to a wire of same material with half the length and double the diameter of the first wire. What will be the change in its length?

Answer 1

Given. l₁ = 4mm = 4 × 10^-3 m

L₂ = L₁/2, D₂ = 2D, r₂ = 2r₁ 

To find : Change in length (l₂)

Calculation: From formula,

Dividing equation (ii) by equation (i),

Since same load is applied on same wire, Y₁ = Y₂ and F₁ = F₂ 

= 0.5 × 10^-3 m 

= 0.5 mm

The new change in length of the wire is 0.5 mm.