Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Newton’s law of universal gravitation is represented by
$F = \frac{G M m}{r^{2}}$
whereF is the magnitude of the gravitational force exerted by one small object on another, $M$ and are the masses of the objects, and $r$ is a distance. Force has the SI units $Kg \cdot {m/s}^{2}$ . What are the SI units of the proportionality constant role="math" localid="1663610883447" $G$ ?

The SI unit of the gravitational constant $G$ is:

$G = \frac{m^{3}}{kg \cdot s^{2}}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Analysis of given data

The formula of the Newton’s law of gravitation is $F = \frac{G M m}{r^{2}},$ where $F$ is the gravitational force, $M$ and $m$ are the masses of bodies, and $r$ is the distance between the bodies. ………..(1)

It has given that the dimension of force is $kg \cdot {m/s}^{2} .$

The analysis of a relationship between different physical quantities by using the units of measurements and dimensions is called dimensional analysis. It is used to examine the correctness of an equation.

Step 2: Write the units of physical quantity

The unit of mass is $kg$

The unit of length is $m$

The unit of time is $s$

Step 3: Determination of units of gravitational constant G

Rewrite the equation (1).

$F = \frac{G M m}{r^{2}}$

Write the SI units for the quantities in the above formula.

$\frac{kg \cdot m}{s^{2}} = \frac{G \cdot kg \cdot kg}{m^{2}}$

Rearrange the above equation for $G$ and cancel the equal terms.

$G = \frac{m^{3}}{kg \cdot s^{2}}$

Hence, the SI unit of the gravitational constant $G$ is:

$G = \frac{m^{3}}{kg \cdot s^{2}} .$

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Analysis of given data

Step 2: Write the units of physical quantity

Step 3: Determination of units of gravitational constant G

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Analysis of given data

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Step 3: Determination of units of gravitational constant G

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