Question

The pressure at the bed of the ocean is $7.84\times {10}^7\mathrm{Pa}$. Find the depth of the ocean.

Answer 1

Step 1: Given data

Pressure at the bed of the ocean, $P=7.84\times {10}^7\mathrm{Pa}$

Step 2: Calculating the depth of the ocean

The pressure $P$ at a depth of $h$ in liquid of density $d$ is given by:

$P=hdg$, where the acceleration due to gravity is denoted by $g=9.8\mathrm{m}/{\mathrm{s}}^2$

The density of water is known to $1000\mathrm{kg}/{\mathrm{m}}^3$

Substituting the known values, the depth of the ocean is calculated as:

$$\begin{gathered} 7.84\times {10}^7=h\left(1000\right)(9.8) \\ h=\frac{7.84\times {10}^7}{1000\times 9.8} \\ =8030\mathrm{m} \\ =8\mathrm{km} \end{gathered}$$

Thus, the depth of the ocean is $8\mathrm{km}$