A well 1km deep is filled with a liquid of density 950kg/m$^3$ and g = 10m/s$^2$, the pressure at the bottom of the well is

Analysis

To find the pressure at the bottom of a well filled with liquid, we need to calculate the hydrostatic pressure. This is the pressure exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity.

Concept

The formula for hydrostatic pressure ($P$) is:

Where:

• $\rho$ (rho) = density of the liquid (in $kg/m^3$)
• $g$ = acceleration due to gravity (in $m/s^2$)
• $h$ = depth of the liquid (in meters)

Solution

Step 1: Identify the given values and ensure they are in SI units.

• Depth ($h$) = $1\text{ km} = 1,000\text{ m} = 10^3\text{ m}$
• Density ($\rho$) = $950\text{ kg/m}^3$
• Gravity ($g$) = $10\text{ m/s}^2$

Step 2: Substitute the values into the formula.

Step 3: Perform the calculation.

Step 4: Convert to standard form. To express $9,500,000$ in standard form, we move the decimal point 6 places to the left:

Conclusion

Comparing our result to the given options, we can see that our calculated value matches option D.

Exam Tip: Always check your units before calculating! JAMB often gives distances in kilometers (km) to test if you remember to convert them to meters (m). Also, remember that $10^6$ is a million; if you get a very large number, standard form is your best friend to avoid counting zeros incorrectly.