In this question, we're shown a hydraulic lift. A lift such as this functions to transmit a smaller force into a larger force via an incompressible liquid. From the diagram shown, we're asked to determine the relative values of the pressure and force on the right and left sides.

A hydraulic lift is able to transmit a small force into a larger force due to the liquid it contains being unable to compress. What this means is that when a force is applied to a given area of the liquid, this pressure is transmitted to all parts of the liquid. Therefore, at any given point, the pressure at all points within the lift will be equal. Thus, we can rule out the answer choices that list pressure.

But what about the forces? If the pressure is the same everywhere in an incompressible liquid, does this also mean the force is the same everywhere? The answer is no. Since pressure depends on the ratio of force to area, equal pressure does not mean equal force, because the area on which the force is acting must be taken into account. We can show this with the following expressions.

As can be seen from the above expression, the output force is greater than the input force by a factor equal to the ratio of the areas on which each force acts. In other words, to maintain constant pressure, a greater area will mean a greater force. Thus, from the diagram, we can see that the force on the right () will be greater than the force on the left ().

Pressure is defined as force divided by area

When the girl is standing on one foot, the force of gravity pulling her down stays the same, but area is cut in half. Thus, pressure is doubled.

Pressure is force divided by area. The force Paul applies is . The rest is just algebra.

Pressure  so the diameter changing does not matter but half the height changes the pressure of the second glass to .

For this question, we're asked to see how the height of a barometer's column will change once the liquid changes from water to mercury.

Barometers are a measure of atmospheric pressure. As the ambient pressure pushes down on the surface of the liquid, this pressure is transmitted throughout the liquid, such that it causes the liquid level in the water to rise. As the ambient pressure increases, the column in the barometer climbs.

We'll need to use the equation for pressure as it relates to density and height.

Since the ambient pressure is the same in both instances, we can set these terms equal to each other. That is to say, it doesn't matter which liquid is being used in the column, because both of them will feel the same pressure from the atmosphere.

Next, we can rearrange the above expression to isolate the term for the height in the mercury column.

Finally, we can plug in the terms given to us in the question stem to arrive at our answer.

Pressure is equal to force over area:

The force will be due to the gravity of the water above. The mass of the water will be the density times the volume.

The volume will be equal to the base area times the length

Combining equations

Plugging in values:

Pressure in a static fluid varies along the axis in which gravity acts. In other words, the deeper one goes, the higher the pressure is. This can be expressed as:

, where h represents the depth. Since we are examining a point 0.1m from the bottom, this is a depth of 0.9m; 0.5 of which is through oil and 0.4 of which is through water. 

Write the density formula. 

The density of air is: 

Find the volume of the freezer in meters. Converting the dimensions from  to  gives.

Solve for the mass of the air.

To answer this question, it's best to start by drawing a free body diagram so that we can identify the forces acting on the cube. Since the cube is submerged in water but not accelerating, we know that we are dealing with a situation in which there is no net force acting on the cube. In the upward direction we have the force caused by the tension in the string as well as the buoyant force of the displaced water. In the downward direction we have the weight of the cube itself.

In order to calculate the buoyant force, we'll need to calculate the volume of the cube in order to determine the amount of water displaced. Since the cube is fully submerged, the volume of the cube will be exactly equal to the volume of displaced water.

Next, plug this value into the above equation for the mass of the cube.

Now that we've found the mass of the cube, we can divide this value by its volume in order to obtain its density.

And lastly, since we have the density of the cube, we can calculate its specific gravity by dividing its density by the density of water.

Use the information given to find the density of the raft. Since the raft is at rest, the forces on it add to zero. Therefore the magnitude of the gravity force is equal to the magnitude of the buoyant force:

The mass of the raft is equal to its density times its volume. We start using subscripts to keep track of which densities and volumes we mean:

The 's cancel, and the  is  of the raft's total volume:

Setting the magnitudes equal again at the Great Salt Lake:

. Cancel the 's and solve for the ratio of submerged volume to total volume of the raft: