test tube filled with water is being spun around in an ultracentrifuge with constant angular velocity \omega. The test tube is lying along a radius and revolving in horizontal plane. The free surface of water is at radius r0 as shown.(a) Show that the pressure at any radius r within the tube is given by:P=(1/2) \rho\omega2 (r2 - r02 ) + Patm(b) Suppose that \omega = 3.8 \times 105 rad/sec and r0 = 10 cm. What is the pressure at r = 13 cm (in atmosphere)? (Does it matter whether it's gauge or atmospheric pressure? )