First slide

Elastic behaviour of solids

Question

A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is

Moderate

A

Equal to that of A
B

Four times that of A
C

Two times that of A
D

Half that of A

Solution

$\begin{array}{l} Stress = \frac{force}{Area} \\ ∴ Stress \propto \frac{1}{{πr}^{2}} \\ \frac{S_{B}}{S_{A}} = {(\frac{r_{A}}{r_{B}})}^{2} = (2)^{2} \Rightarrow S_{B} = 4 S_{A} \end{array}$

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