Properties of Matter 1 Question 10
10. One end of a horizontal thick copper wire of length $2 L$ and radius $2 R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
(a) 0.25
(b) 0.50
(c) 2.00
(d) 4.00
(2013 Adv.)
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Answer:
Correct Answer: 10. (c)
Solution:
$$ \begin{aligned} & \Delta l=\frac{F L}{A Y}=\frac{F L}{\left(\pi r^2\right) Y} \\ & \Rightarrow \Delta l \propto \frac{L}{r^2} \\ & \therefore \quad \frac{\Delta l_1}{\Delta l_2}=\frac{L R^2}{2 L(2 R)^2}=2 \end{aligned} $$
