Two identical containers, A and B, are filled to the rim with different liquids.

Question

Two identical containers, A and B, are filled to the rim with different liquids. Two identical plastic blocks float in the corresponding containers as shown in the figure below. Is the buyoant force on the block by Liquid A greater than, less than, or equal to the buyoant force on the block by Liquid B? Points P and R are points in the corresponding liquids at the bottom of each block. Is the pressure at P greater than, less than or equal to that at R? Explain your reasoning. Each container is placed on a scale. Is the scale reading for container A greater than, less than or equal to that of container B? Explain your reasoning. (Hint: Think of (what else ?) the free-body diagram of a conveniently chosen object!) A pipe with a closed valve is placed between two containers. When the valve is opened, which container, if either, will overflow? Explain your reasoning.

Explanation / Answer

a). Buoyant force is same as for both the blocks it is equal to mg

b). Pressure at P and R is equal

Since buoyancy is same,

density of liquid*submerged volume of body is same

as both the blocks have same crassectional area,

density of liquid*submerged height of body is same

Presure = density of liquid*depth of point*g

in this case it is

Presure = density of liquid*submerged height of body*g which is same

So pressure is same

c). So now we know density of liquid*submerged height of body is same here i.e liquid B is denser

since both containers have same volume, container A will be lighter

d). as we know liquid B is denser and

Presure = density of liquid*depth of point*g

we can see pressure at same depth will be higher for B

and Since fluid flow from high pressure to low pressure, Liquid B will move to container A and container A will overflow.

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