Fluid Basics

There are two identical containers A and B on a table, each containing a solid wooden sphere and a solid copper sphere of equal volume. The containers are filled with equal masses of water and alcohol, respectively. The density relationship among water, alcohol, the wooden sphere, and the copper sphere is:

The wooden sphere is placed into the water, and the copper sphere is placed into the alcohol (no liquid overflows). After the system comes to rest, the pressures exerted by containers A and B on the table are $p_1$ and $p_2$, respectively, and the buoyant forces on the wooden sphere and the copper sphere are $F_1$ and $F_2$, respectively.

There is a cup filled with water. A pingpong is floating on top of it. The pingpong is pushed to the bottom of the cup with pingpong fully submerged. At $t=0$, the pingpong is let go, and it goes up and jumps out of the water before coming back down.

On the table there are two cups, each with different liquid filled all the way to the top. The density of the liquid in cup A and B are $\rho_A$ and $\rho_B$, respectively, but are unknown. Now a solid ball with density $\rho_0$ is gently dropped into the liquid A, the ball is floating on the surface with mass of the overflown liquid $m_A$. When the same ball is dropped into liquid B, the ball sinks to the ball, with $m_B$ liquid overflown.

There is water in a container. A plastic test tube has a small iron block hanging underneath it, and the test tube floats on the water surface. Now the small iron block is removed and placed inside the test tube, and the test tube still floats on the water surface. Then:

There is a solid spherical object. When weighed in air using a spring scale, the scale reads 12 N. When half of the object’s volume is immersed in water, the spring scale reads 5 N. If the object is then gently released into the water so that it floats freely at equilibrium, the buoyant force acting on the object will be:

A thin-walled container with a flat bottom has a base area of $2.0 \times 10^{-2}\text{m}^2$. It contains an appropriate amount of water. A solid object is placed into the water in the container, and when the object comes to rest, it floats on the water surface. The volume of the part of the object submerged in the water is $1.8 \times 10^{-3}\,\text{m}^3$, and the water level in the container rises by 6 cm (no water overflows). Water density is $1.0 \times 10^3\,\frac{kg}{m^3}$$. Find: