Question

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown.

The force stretches the combination by $10mm$. How far does the midpoint A move. (in mm)

Answer 1

Answer: 8

$\frac{F}{A_1}=y\frac{\Delta {\ell }_1}{\ell }$
$\frac{F}{A_2}=y\frac{\Delta {\ell }_2}{\ell }$
$\Delta {\ell }_1+\Delta {\ell }_2=10mm$
$\frac{F\ell }{A_{1}y}+\frac{F\ell }{4A_{1}y}=10mm$
$\frac{F\ell }{A_{1}y}+\frac{F\ell }{4A_{1}y}=10mm$
$\Rightarrow \frac{F\ell }{A_{1}y}=8mm$