Question

Whales can dive undersea to depths of 2 km. The pressure on the whale at this depth (ignoring atmospheric pressure) is _____ $× 10^6 Pa$. (Density of sea water = $1 g cm^{-3}$ and $g =10 m s^{-2}$)

Answer 1

Correct Answer: 20

To determine the pressure exerted on a whale diving 2 km under the sea, we first convert given units and apply fundamental physics principles. The depth is \(2 \, \text{km} = 2000 \, \text{m}\). The pressure due to a fluid column is calculated using the formula:

\( P = \rho \cdot g \cdot h \)

where \( \rho \) is the density of the fluid, \( g \) is the acceleration due to gravity, and \( h \) is the depth.

Given:

• Density of sea water, \( \rho = 1 \, \text{g/cm}^3 = 1000 \, \text{kg/m}^3\)
• Acceleration due to gravity, \( g = 10 \, \text{m/s}^2\)
• Depth, \( h = 2000 \, \text{m}\)

Substituting these values into the formula:

\( P = 1000 \cdot 10 \cdot 2000 = 20,000,000 \, \text{Pa} \) or \( P = 2 \times 10^7 \, \text{Pa}\)

Finally, since we need the pressure in terms of \( \times 10^6 \, \text{Pa}\), we rewrite:

\( P = 20 \times 10^6 \, \text{Pa}\)

This value falls within the specified range of 20,20. Therefore, the pressure on the whale at this depth is:

\( \text{Pressure} = 20 \times 10^6 \, \text{Pa}\)