Question

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

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

College Physics

College Physics

Paul Peter Urone,… 1st Edition

Chapter 11, Problem 16

Instant Answer

Solved by Expert Mayukh Banik

07/02/2020

Step 1

The SI unit of height ($h$) is meter (m), the SI unit of density ($\rho$) is kilogram per cubic meter (kg/m³), and the SI unit of gravity ($g$) is meter per second squared (m/s²). Show more…

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

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Key Concepts

Pressure (Pascal)

Pressure is defined as force per unit area, and its SI unit is the Pascal (N/m²). Recognizing that the product of h, ?, and g results in units that correspond to force distributed over an area is essential for understanding how these physical quantities relate to pressure in various contexts.

Basic Physical Quantities

In the context of the expression h?g, the quantities include height (h) measured in meters, density (?) measured in kilograms per cubic meter, and gravitational acceleration (g) measured in meters per second squared. Knowing the SI units for these fundamental quantities is key to combining them appropriately to obtain a resultant unit.

Dimensional Analysis

Dimensional analysis is a method to verify the consistency of units in a physical equation. By analyzing the fundamental dimensions—such as length, mass, and time—this technique ensures that the computed units on both sides of an equation match, confirming the equation's validity.

SI Units and Unit Conversion

SI units provide a standardized system of measurements for physical quantities. Each unit, whether it is for length (meter), mass (kilogram), or time (second), can be combined to form derived units that are essential for consistently expressing physical relationships. Understanding how to convert between base units and derived units is crucial when verifying unit consistency in physical equations.

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