Question 275: Properties of Matter

Question

A wire of length $$\mathrm{L}$$ and radius $$\mathrm{r}$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$\mathrm{F}$$, its length increases by $$5 \mathrm{~cm}$$. Another wire of the same material of length $$4 \mathrm{L}$$ and radius $$4 \mathrm{r}$$ is pulled by a force $$4 \mathrm{F}$$ under same conditions. The increase in length of this wire is __________________ $$\mathrm{cm}$$.

Accepted Answer

$${{F/A} \over {\Delta L/L}} = Y$$
$$ \Rightarrow \Delta L = {{FL} \over {AY}}$$
$${{\Delta {L_2}} \over {\Delta {L_1}}} = \left( {{{{F_2}} \over {{F_1}}}} ight) 	imes \left( {{{{L_2}} \over {{L_1}}}} ight) 	imes \left( {{{{A_1}} \over {{A_2}}}} ight)$$
$$ = 4 	imes 4 	imes {1 \over {16}} = 1$$
$$\Delta {L_2} = \Delta {L_1} = 5$$ cm.

Properties of Matter

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