First slide

Elastic behaviour of solids

Question

Two wires of the same material have lengths in the ratio 1:2 and their radii are in the ratio $1 : \sqrt{2}$ . If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

Moderate

A

$\sqrt{2} : 2$
B

$2 : \sqrt{2}$
C

$1 : 1$
D

$1 : 2$

Solution

$\begin{array}{l} Y = \frac{Fl}{{πr}^{2} Δl} or Δl = \frac{Fl}{{πr}^{2} Y} \\ Δl \propto \frac{1}{r^{2}}, {Δl}^{'} \propto \frac{2 l}{(\sqrt{2} r)^{2}} or {Δl}^{'} \propto \frac{l}{r^{2}} \\ ∴ \frac{Δl}{{Δl}^{'}} = 1 : 1 \end{array}$

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