JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 23)
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 __________________ $$\mathrm{cm}$$.
Answer
5
Explanation
$${{F/A} \over {\Delta L/L}} = Y$$
$$ \Rightarrow \Delta L = {{FL} \over {AY}}$$
$${{\Delta {L_2}} \over {\Delta {L_1}}} = \left( {{{{F_2}} \over {{F_1}}}} \right) \times \left( {{{{L_2}} \over {{L_1}}}} \right) \times \left( {{{{A_1}} \over {{A_2}}}} \right)$$
$$ = 4 \times 4 \times {1 \over {16}} = 1$$
$$\Delta {L_2} = \Delta {L_1} = 5$$ cm.
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