Question

the pressure at (10\text{ m}) below the surface of the ocean is about (2.00 \times 10^5\text{ pa}).

part a
which of the following statements is true?

• the weight of a column of seawater (1\text{ m}^2) in cross section and (10\text{ m}) high is about (2.00 \times 10^5\text{ n}).
• the weight of a column of seawater (1\text{ m}^2) in cross section and (10\text{ m}) high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about (2.00 \times 10^5\text{ n}).
• the weight of (1\text{ m}^3) of seawater at (10\text{ m}) below the surface of the ocean is about (2.00 \times 10^5\text{ n}).
• the density of seawater is about (2.00 \times 10^5) times the density of air at sea level.

part b
now consider the pressure (20\text{ m}) below the surface of the ocean. which of the following statements is true?

• the pressure is twice that at a depth of (10\text{ m}).
• the pressure is the same as that at a depth of (10\text{ m}).
• the pressure is equal to that at a depth of (10\text{ m}) plus the weight per (1\text{ m}^2) cross sectional area of a column of seawater (10\text{ m}) high.
• the pressure is equal to the weight per (1\text{ m}^2) cross sectional area of a column of seawater (20\text{ m}) high.

Explanation:

Analyze Part A using pressure definition

$$ P = \frac{F}{A} \implies F = P \cdot A $$

$$ P = 2.00 \times 10^5 \text{ Pa},\quad A = 1 \text{ m}^2 \implies F = 2.00 \times 10^5 \text{ N} $$

The total force \(F\) is the total weight of the fluid column (air column plus seawater column) above that area.

Analyze Part B using hydrostatic pressure relation

$$ P(h) = P_0 + ho g h $$

$$ P(20\text{ m}) = P(10\text{ m}) + ho g (10\text{ m}) $$

The term \(
ho g (10\text{ m})\) represents the weight per \(1\text{ m}^2\) cross-sectional area of a column of seawater \(10\text{ m}\) high.

Answer:

Question 1

• (A) The weight of a column of seawater \(1\text{ m}^2\) in cross section and \(10\text{ m}\) high is about \(2.00 \times 10^5\text{ N}\).
• (B) The weight of a column of seawater \(1\text{ m}^2\) in cross section and \(10\text{ m}\) high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about \(2.00 \times 10^5\text{ N}\). (Correct answer)
• (C) The weight of \(1\text{ m}^3\) of seawater at \(10\text{ m}\) below the surface of the ocean is about \(2.00 \times 10^5\text{ N}\).
• (D) The density of seawater is about \(2.00 \times 10^5\) times the density of air at sea level.

Question 2

• (A) The pressure is twice that at a depth of \(10\text{ m}\).
• (B) The pressure is the same as that at a depth of \(10\text{ m}\).
• (C) The pressure is equal to that at a depth of \(10\text{ m}\) plus the weight per \(1\text{ m}^2\) cross-sectional area of a column of seawater \(10\text{ m}\) high. (Correct answer)
• (D) The pressure is equal to the weight per \(1\text{ m}^2\) cross-sectional area of a column of seawater \(20\text{ m}\) high.