First slide

Elastic behaviour of solids

Question

When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be

Moderate

A

0.5 cm
B

2 cm
C

4 cm
D

8 cm

Solution

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

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