Question

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

The force stretches the combination by $\frac{27}{4} \,mm$. How far (in $mm$ ) does the junction point $A$ move?

Answer 1

$\frac{F}{A_{1}}=Y \frac{\Delta l_{1}}{2 L}$
$\frac{F}{A_{2}}=Y \frac{\Delta l_{2}}{L}$
$\Delta l_{1}+\Delta l_{2}=\frac{27}{4}\, mm$
$\frac{2 F L}{A_{1} Y}+\frac{F L}{4 A_{1} Y}=\frac{27}{4}\, mm$