First slide

Elastic behaviour of solids

Question

Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is

Moderate

A

Four times for wire A as for wire B
B

Twice for wire A as for wire B
C

Half for wire A as for wire B
D

One-fourth for wire A as for wire B

Solution

$\begin{array}{l} l = \frac{FL}{AY} \Rightarrow l \propto \frac{1}{r^{2}} (\underline{\underline{F}, L} and Y are same) \\ \frac{l_{A}}{l_{B}} = {(\frac{r_{B}}{r_{A}})}^{2} = {(\frac{r_{B}}{2 r_{B}})}^{2} = \frac{1}{4} \Rightarrow l_{B} = 4 l_{A} or l_{A} = \frac{l_{B}}{4} \end{array}$

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