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Verify that the SI unit of $h\rho g$ is $\textrm{N/m}^2$.
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 11, Problem 16 (Problems & Exercises) (1:11)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We are going to verify that the units of height multiplied by density multiplied by acceleration due to gravity is the same as newtons per meter squared or pressure in other words. So replacing the height with its unit of meters and density with its unit of kilograms per cubic meter and g is meters per second squared and on the right hand side, we can work on this too and we can say that newtons which comes from Newton's second law, F equals ma, is kilograms multiplied by meters per second squared so that's what I have written here and then this is meters squared on the top canceling two of the meters here leaving meters to the power of 1 on the bottom and second squared is on the bottom and kilograms is on the top. And on this side over here, we can multiply the top by second squared per meter and that makes these units cancel entirely on the top then multiply the bottom by second squared per meter canceling one of the meters and leaving us with a second squared so we have kilograms per meter second squared on the right as well and since we have been able to make both sides the same, we can say that they are the same.