Question

Two wires a and b, of the same material, have their lengths in their ratio of 1:2 and them diameters in the ratio of 2:1. if they are stretched with the same force, the ratio of the increases in the lengths of a and that b will be

Answer 1

The lenght of the frame is 25 meter

Answer 2

Answer:

$\frac{1}{8}$

Explanation:

Since both the wires are of the same material , their Young's Moduli are equal.

Therefore,

$\frac{stress}{strain} =constant$

$\frac{F/A}{Δl/l} =constant$

Since force applied is same ,

$\frac{l}{A(dl)} =constant$

substituting the values, taking area proportional to square of diameter

$\frac{1}{4a} =\frac{2}{b}$

$\frac{a}{b} =\frac{1}{8}$