Question

The pressure at the bed of the ocean is $7.84\times {10}^{7}Pa.$Find the depth of the ocean. Density of water is ${10}^{3}kg{m}^{-3}$and $g=10m/s^2$

Answer 1

Step1: Given data

Pressure at the bed of the ocean (P) = $7.84\times {10}^{7}Pa.$

The density of water (d) = ${10}^{3}kg{m}^{-3}$

Acceleration due to gravity (g) = $10m/s^2$

Depth of ocean (h) =?

Step2: Formula used

$$\begin{gathered} Pressure=height\times density\times gravity \\ P=hdg............\left(a\right) \end{gathered}$$

Step3: Calculating the depth of the ocean bed:

Putting all the given values in equation (a)

$$\begin{gathered} h=\frac{P}{dg}=\frac{7.84\times {10}^{7}Pa}{{10}^{3}kg{m}^{-3}\times 10m/s^2} \\ h=7.84\times {10}^{3}m \\ h=7840m \end{gathered}$$

Hence, the depth of the ocean bed is 7840 m.