Question

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. 0.5
• C. 2
• D. 4

Answer 1

Answer: (C)

2

Answer 2

$k _{1}=\frac{\pi 4 R ^{2} x }{2 L },$
$k _{2}=\frac{\pi R ^{2} y }{ L }$
$F = k _{1}\, x = k _{2} \,y$
$\Rightarrow \frac{ y }{ x }=\frac{ k _{1}}{ k _{2}}=2$