If the reactor in Problem $7\mathrm{.}19$ is controlled by an array of $25$ more or less uniformly distributed black rods $0\mathrm{.}3$ in$.$ in diameter, what is the total worth of the rods?

An experimental reactor facility is a bare square cylinder $100cm$ high, composed of small beryllium blocks with thin foils of ${?}^{235}U$ placed in between, so that the system can be considered to be a homogeneous mixture of $Be$ and ${?}^{235}U.$ The reactor is to be controlled with a single black control rod $2\mathrm{.}5cm$ in radius and located along the axis of the system. $($a$)$ If the reactor is critical with the rod fully withdrawn, how much negative reactivity is introduced into the system when the rod is fully inserted? $($b$)$ Assuming that the rod moves into the reactor instantaneously, on what period does the reactor go$?$