Problem $7\mathrm{.}6\mathrm{.}7$

A rubber cylinder $R$ of length $L$ and cross$-$

$($a$)$ Derive a formula for the lateral pressure between the rubber and the steel.

Disregard friction between the rubber and the steel, and assume that the steel cylinder is rigid when compared to the rubber. sectional area $A$ is compressed inside a steel cylinder $S$ by a force $F$ that applies a uniformly distributed pressure to the rubber.

$($b$)$ Derive a formula for the shortening of the rubber cylinder.