$(30$ points$)$ The closed cylindrical tank has diameter of $0\mathrm{.}6$ m and length of

$1\mathrm{.}2$ m $.$ The tank contains liquid hydrogen with a specific weight of $694\mathrm{.}8$

$\frac{N}{m^3},$ and it rotates about its vertical axis at $100$ RPM$.$ a$)$ Determine the

pressure difference $P_A-P_B.$ b$)$ If in addition to the rotation, the tank is

accelerated upward at $a_z=3\frac{m}{s},$ determine the pressure difference $P_A-P_B.$