$4($e$)$ Consider two concentric circular cylinders x and Y of different

materials in contact with each other at radius r$=$b$.$ The compound

cylinder is subjected to an internal pressure P$.$ If the radial and

tangential displacement in the cylinder x is $($u$\_($r$)^($x$),$u$\_(\backslash$theta $)^($x$))$ and in

cylinder Y is $($u$\_($r$)^($Y$),$u$\_(\backslash$theta $)^($Y$)).$ The displacement boundary condition that

needs to be satisfied at the frictionless interface of the two cylinders

is