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 $10\ mm$. How far does the midpoint $A$ move ............ $mm$
Diffcult
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$\frac{F}{A_{1}}=Y \frac{\triangle l_{1}}{\lim }$ plies $\triangle l-1=\frac{F l}{A_{1} Y}$
$\frac{F}{A_{2}}=Y \frac{\triangle l_{2}}{\lim }$ plies $\triangle l-2=\frac{F l}{A_{2} Y}=\frac{F l}{4 A_{1}}=8 m m$
$\Delta l-1+\triangle l_{2}=10 m m$
$\frac{F l}{A_{1} y}+\frac{F l}{4 A_{1} Y}=10 m m \Rightarrow \frac{F l}{A_{1} Y}=8 m m$
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