$(15$ points, based on Example $4\mathrm{.}17)$ A micro actuator is made of a bilayer strip $-$ a silicon layer

with a polyimide film on top. A very thin resistance heating film is deposited between the two

layers. If the two layer strip is subjected to a uniform temperature rise $T=10C,$

$($a$)$ Calculate the radius of curvature $($do not use wrong equation $(4\mathrm{.}51)$ in the textbook$).$

$($b$)$ Calculate the interfacial force between the Si and the polyimide layer $($do not use wrong

equation $(4\mathrm{.}50)$ in the textbook$).$

$($c$)$ Calculate the displacement of the free end.