The total pressure on the ball includes both hydrostatic and atmospheric pressure:

We are given the atmospheric pressure, so we just need to determine the hydrostatic pressure using the following expression:

Plugging in values:

Therefore,

Now to determine the force on the ball, we need it's surface area. For a sphere:

Then,

We can calculate the total pressure on the ball from the given force and radius:

Where for a sphere:

There are two pressures that combine to the total pressure on the ball: hydrostatic and atmospheric. 

Since the ball is submerged in the ocean, we know that the surface of the water is at sea level and thus has a pressure:

Also, we can calculate the hydrostatic pressure with the following expression:

Where density is of the ocean and the height is the depth of the ball. Plugging this into our last expression, we get:

Rearranging for height:

To determine the hydrostatic pressure, we need to know the depth of the ship at time t = 12s. We can determine this with the following expression:

Then using the expression for hydrostatic pressure:

Given the hydrostatic pressure, we can calculate the depth that this occurs at:

Rearranging for height:

Plugging in our values, we get:

We can then use the following kinematics equation to determine how much time has passed:

If we designate the downward direction as positive and plugging in values to the kinematics equation, we get:

Rearranging, we get:

Since we can't have a negative time, the first one is the answer.

We will use the expression for hydrostatic pressure for this problem:

In this scenario, the pressures from each material are additive. Therefore:

Plugging in expressions:

Plugging in values:

Note how we used 0.9m for the height of mercury since we are asked for the pressure at a height of 0.5m.

The following formula on pressure and area is used:

We substitute our known values and solve for F2 to obtain the output force:

Therefore the correct answer is  of force.

The formula for pressure is given as:

Where  is pressure in pascals,  is force in newtons, and  is area in meters squared. By substituting our known values we can solve for pressure:

Therefore the correct answer is 

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.