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Pressure in a Centrifuge

A test tube filled with liquid of uniform density rho, as shown in the figure (see attachment), is spun in a centrifuge with angular frequency w. The test tube lies perpendicular to the axis of rotation of the centrifuge. The pressure in the fluid at the distance r0 from the axis of rotation is p0. You may ignore the variation in pressure with depth; assume that it is much smaller than the variation in pressure with radius.

a). What is the pressure p(r) of the fluid in the test tube at an arbitrary distance r from the axis of rotation?(Express your answer in terms of rho, r, omega, r0, and p0)


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