Problem $2\mathrm{.}4-10$

A plastic rod $AB$ of length $L=0\mathrm{.}5m$ has a diameter $d_1=30mm($see figure$).$ A plastic sleeve $CD$ of

length $c=0\mathrm{.}3m$ and outer diameter $d_2=45mm$ is securely bonded to the rod so that no slippage can

occur between the rod and the sleeve. The rod is made of an acrylic with a modulus of elasticity $E_1=3\mathrm{.}1$GPa,

and the sleeve is made of a polyamide with $E_2=2\mathrm{.}5$GPa.

$($a$)$ Calculate the elongation $$ of trie rou wrieri is is puneu dy axia ioices $r=\frac{1}{{?}_k}Iv.$

$($b$)$ If the sleeve is extended for the full length of the rod, what is the elongation?

$($c$)$ If the sleeve is removed. what is the elongation?