(a) In experimental reactors, the control rod worth is measured using the change in geometric buckling. Assuming that only the leakage or geometrical buckling changes in such an experiment, derive an expression for its reactivity worth as a function of this buckling.

(b) A spherical reactor using a homogeneous solution of \({ }^{235} \mathrm{U}\) and heavy water is critical with a volume of \(50 \mathrm{~cm}^{3}\). Calculate the reactivity, if the volume of the solution is increased by \(5 \mathrm{~cm}^{3}\) (use \(M^{2}=40 \mathrm{~cm}^{2}\) ).