Question

The pressure at 10
The pressure at 10 m below the surface of the ocean is about2.00�10^5 Pa. Which of the following statements istrue? The weight of a column of seawater 1 m^2 in cross section and 10 m high is about 2.00�10^5 N. The weight of a column of seawater 1m^2 in cross section and 10 m high plus the weight of a column of air with thesame cross section extending up to the top of the atmosphere isabout 2.00�10^5 N The weight of 1 m^3 of seawater at 10 m below the surface of the ocean is about2.00�10^5 N.Now consider he pressure at 20 m below the surface of the ocean.The density of seawater is about2.00�10^5 times the density of air at sealevel. This pressure is twice that at a depth of 10 m.the same as that at a depth of 10 m. equal to that at a depth of 10 m plus the weight of a column of seawater 1 m^2 in cross section and 10 m high. equal to the weight of a column of seawater 1m^2 in cross section and 20 m high
below the surface of the ocean is about2.00×10⁵.

Which of the following statements istrue?

The weight of a column of seawater 1 ${\rm m}^2$ in cross section and 10 ${\rm m}$ high is about 2.00×105 $\rm N$ . The weight of a column of seawater 1 ${\rm m}^2$ in cross section and 10 ${\rm m}$ high plus the weight of a column of air with thesame cross section extending up to the top of the atmosphere isabout 2.00×105 $\rm N$ . The weight of 1 ${\rm m}^3$ of seawater at 10 ${\rm m}$ below the surface of the ocean is about2.00×105 $\rm N$ . The density of seawater is about2.00×105 times the density of air at sealevel.

Now consider he pressure at 20 ${\rm m}$ below the surface of the ocean.

This pressure is

twice that at a depth of 10 The pressure at 10 m below the surface of the ocean is about2.00�10^5 Pa. Which of the following statements istrue? The weight of a column of seawater 1 m^2 in cross section and 10 m high is about 2.00�10^5 N. The weight of a column of seawater 1m^2 in cross section and 10 m high plus the weight of a column of air with thesame cross section extending up to the top of the atmosphere isabout 2.00�10^5 N The weight of 1 m^3 of seawater at 10 m below the surface of the ocean is about2.00�10^5 N.Now consider he pressure at 20 m below the surface of the ocean.The density of seawater is about2.00�10^5 times the density of air at sealevel. This pressure is twice that at a depth of 10 m.the same as that at a depth of 10 m. equal to that at a depth of 10 m plus the weight of a column of seawater 1 m^2 in cross section and 10 m high. equal to the weight of a column of seawater 1m^2 in cross section and 20 m high . the same as that at a depth of 10 ${\rm m}$ . equal to that at a depth of 10 ${\rm m}$ plus the weight of a column of seawater 1 ${\rm m}^2$ in cross section and 10 ${\rm m}$ high. equal to the weight of a column of seawater 1 ${\rm m}^2$ in cross section and 20 ${\rm m}$ high.

Answer 1

Concepts and reason

The concept used to solve this problem is variation of pressure with depth in a fluid.

First use relation of atmospheric pressure and static fluid pressure to calculate the total pressure

Finally use the relation between total pressure and area to calculate the force.

Fundamentals

If a fluid is within a container then the depth of an object placed in that fluid can be measured.

Expression for the weight of the object is,

Here, W is the weight of the object, m is the mass of the object and g is the acceleration due to gravity.

Volume of the object is,

Here, A is the area of the object and h is the depth of fluid.

Expression for the force is,

Here, F is the force.

Expression for the static fluid pressure is,

Here, is the static fluid pressure.

If the container is open to the atmosphere above, the atmospheric pressure must be added to get the total pressure.

Expression for the total pressure is,

Here, is the total pressure and is the atmospheric pressure.

(1)

Expression for the total pressure is,

Here, is the total pressure at below the surface of the ocean.

Substitute for and for .

Expression for the force is,

Here, F is the force.

Substitute for and for A.

(2)

Expression for the static fluid pressure is,

Consider the pressure at 20 m below the surface of the ocean. Since, the pressure at 20 m surface will be pressure at 10 m surface plus the pressure of the 10 m surface below the top 10 m surface.

Thus, this pressure must be equal to that at a depth of plus the weight of a column of seawater in cross section and high.

Ans: Part 1

The weight of a column of seawater in cross section and high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about .