First slide

Elastic behaviour of solids

Question

Two bars A and B of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of A to that of B will be

Moderate

A

16
B

8
C

4
D

2

Solution

We have, $Y = \frac{Fl}{aΔl}$
$\Rightarrow Y = \frac{F}{a} \times \frac{l}{Δl}$
$Now, V = al or l = \frac{V}{a} ∴ Y = \frac{FV}{a^{2} Δl}$
$\begin{array}{l} Δl \propto \frac{1}{a^{2}} or Δl \propto \frac{1}{D^{4}} \\ \frac{{Δl}_{A}}{{Δl}_{B}} = \frac{D_{B}^{4}}{D_{A}^{4}} = \frac{1^{4}}{{(\frac{1}{2})}^{4}} = 16 \end{array}$

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