Bukhovtsev-et-al-Problems-in-Elementary-Physics

MECHANICS 67
286. In Problem 285, the velocity v may become infinitely
high even with a small force F when a ~ A. Explain this paradoxical
phenomenon...
287. A water clock (clepsydra) used in ancient Greece is designed
as a vessel with a small orifice 0 (Fig. 120). The time
is determined according to the level of the water in the vessel.
What should the shape of the vessel be for the time scale to
be uniform?
288. A cylindrical vessel with a liquid rotates with an angular
velocity ro around a vertical axis (Fig. 121). Determine the
change of pressure in the horizontal cross section of the vessel
depending on the distance to the axis of rotation.
Note. Apply the method described in solving Problem 203.
289. Find the shape of the surface of a liquid in a cylindrical
vessel rotating with an angular velocity ro around a vertical
axis (Le., the height of the liquid level depending on the distance
to the axis of rotation).
290. Why do the tea leaves gather in the middle of a glass
after stirring?