This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 3

2017 F = ma, 9
Tags: fluids
Flasks A, B, and C each have a circular base with a radius of 2 cm. An equal volume of water is poured into each flask, and none overflow. Rank the force of water F on the base of the flask from greatest to least. A) $F_A > F_B > F_C$ B) $F_A > F_C > F_B$ C) $F_B > F_C > F_A$ D) $F_C > F_A > F_B$ E) $F_A = F_B = F_C$

2017 F = ma, 10
Tags: fluids , pressure
10) The handle of a gallon of milk is plugged by a manufacturing defect. After removing the cap and pouring out some milk, the level of milk in the main part of the jug is lower than in the handle, as shown in the figure. Which statement is true of the gauge pressure $P$ of the milk at the bottom of the jug? $\rho$ is the density of the milk. A) $P = \rho gh$ B) $P = \rho gH$ C) $\rho gH< P < \rho gh$ D) $P > \rho gh$ E) $P < \rho gH$

1960 Putnam, B3
Tags: motion , physics , fluids
The motion of the particles of a fluid in the plane is specified by the following components of velocity $$\frac{dx}{dt}=y+2x(1-x^2 -y^2),\;\; \frac{dy}{dt}=-x.$$ Sketch the shape of the trajectories near the origin. Discuss what happens to an individual particle as $t\to \infty$, and justify your conclusion.