In this worksheet, we will practice comparing an object's weight to the weight of the fluid displaced by the object and we will explain how this determines an object's buoyancy.

**Q1: **

A submarine under the sea has a lower density than the seawater around it,
which is
kg/m^{3}, because most
of the submarine’s volume consists of air that has a density of
1.225 kg/m^{3}. If 90% of the
submarine’s volume is air and 10% of its volume is steel of density
kg/m^{3}, how many times
greater is the upthrust force that the water applies to the submarine than the
submarine’s weight? Round your answer to one decimal place.

**Q2: **

A cube-shaped object, with sides that are
130 cm long each, has a density of
950 kg/m^{3}. The cube is placed into a
body of water. The water has a density of kg/m^{3}.

What is the volume of the object in cubic meters?

- A
1.3 m
^{3} - B
1.69 m
^{3} - C
9.2 m
^{3} - D
2.197 m
^{3} - E
10.14 m
^{3}

What is the mass of the object? Answer to the nearest kilogram.

How many cubic meters of water have a mass equal to that of the object?

How far below the water’s surface must the base of the object be in order to displace a mass of water equal to that of the object? Answer to the nearest centimeter.

**Q3: **

A cuboid-shaped object floats at rest in water of density 1 000 kg/m^{3}. The top of the object is at a depth of 2.5 m and its base is at a depth of 5.5 m.

How much greater is the pressure exerted by water at the object’s base than at its top?

The horizontal faces of the object both have an
area of 0.25 m^{2}. How much greater is the force exerted by water at
the object’s base than at its top?

**Q10: **

A cylindrical object is at rest in water with its top circular face just at the water’s
surface, as shown in the diagram. The water pressure at the base of the object is 1 200 Pa.
The area of a circular face of the object is 2.45 m^{2}. What must the mass of the
object be for its weight to be equal to the force that the water exerts on the submerged
circular face of the object?

**Q11: **

An object is submerged at rest in water of density 1 000 kg/m^{3}. The top of the object is 1.8 m below the water surface and its base is 7.2 m below it. The square-shaped area of the base and of the top of the object are both 1.5 m^{2}.

What pressure from the water acts on the top of the object?

What pressure from the water acts on the base of the object?

What force from the water pressure acts on the top of the object?

What force from the water pressure acts on the base of the object?

What is the weight of the object?

What is the mass of the object?

What is the volume of the object?

What is the density of the object? Answer to the nearest kilogram per cubic meter.

What mass of water does the object displace?

If the top of the object was 5.4 m below the surface while its base was 7.2 m below it, and the object’s weight did not change, what would the instantaneous downward acceleration of the object be?