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Q12P

Expert-verifiedFound in: Page 16

Book edition
9th Edition

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

Pages
1624 pages

ISBN
9781133947271

**Newton’s law of universal gravitation is represented by **

** ${F}{=}\frac{GMm}{{r}^{2}}$**

**where F is the magnitude of the gravitational force exerted by one small object on another, ${M}$**

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

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

The formula of the Newton’s law of gravitation is** $F=\frac{GMm}{{r}^{2}},$** 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 $\text{kg}\cdot {\text{m/s}}^{\text{2}}.$

**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.**

The unit of mass is $\text{kg}$

The unit of length is $\text{m}$

The unit of time is $\text{s}$

** Rewrite the equation (1).**

**$F=\frac{GMm}{{r}^{2}}$**

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

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

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

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

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

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

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