Consider a Cherenkov apparatus to be operated as a threshold counter. The pressure of the N2 gas it contains can be varied. The index n depends on the pressure π, measured in pascal, as n=1+3 x 10^-9 π. A beam composed of π⁺s, K⁺s and protons all with momentum p crosses the counter. Knowing that π⁺s are above threshold for π≥5.2 x 10³ Pa: 

(a) Find the momentum p; 

(b) Find the minimum pressure at which the K⁺s are above threshold; 

(c) Find the same for the protons. p is much larger than the mass of each species.