Question

Two parallel steel wires A and B are fixed to rigid support at the upper ends and subjected to the same load at the lower ends . the lengths of wires are in the ratio 4:5 and their radii are in the ratio 4:3. the increase in the length of wire A is 1 mm. calculate the increase in length of wire B

Answer 1

This question is based on mechanical properties of matters.

Let length of wire A is L and wire B is L' .
according to question,
L/L' = 4/5 ......(1)
and R/R' = 4/3 .......(2)
increase in length of wire A , ∆L = 1mm

we know from formula of Young's modulus,
Y = FL/A∆L

as the material is same . so, Young's modulus in both cases will be same.
e.g., $Y_1=Y_2$

$\frac{FL}{A\Delta{L}}=\frac{FL'}{A'\Delta{L'}}$

$\frac{L}{\pi R^2\times\Delta{L}}=\frac{L'}{\pi R'^2\times\Delta{L'}}$

L/R²∆L = L'/R'²∆L'

(L/L')/(R/R')² = ∆L/∆L'

(4/5)/(4/3)² = 1mm/∆L

∆L = 20/9 mm = 2.22 mm