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Found in: Page 439

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# Two objects attract each other with a gravitational force of a magnitude $1.00×{10}^{-8}\text{N}$when separated by 20.0 cm. If the total mass of the two objects is 5.00 kg, what is the mass of each?

The masses of objects are ${m}_{1}=3.00kg$and ${m}_{2}=2.00kg$ .

See the step by step solution

## Step 1: Newton’s Law

Newton’s law of universal gravitation states that the gravitational force of attraction between any two particles of masses ${M}_{1}$and ${M}_{2}$ separated by a distance r has the magnitude:

${F}_{g}=G\frac{{m}_{1}.{m}_{2}}{{r}^{2}}$

Where, $G=6.674×{10}^{-11}\text{N}·{\text{m}}^{\text{2}}{\text{/kg}}^{\text{2}}$ is the universal gravitational constant. This equation enables us to calculate the force of attraction between masses under many circumstances.

## Step 2: Given

Gravitational force: ${F}_{g}=1.00×{10}^{-8}\text{N}$

Distance between two objects: $r=20\text{cm}=0.2\text{m}$

## Step 3: Find the masses

We find the reason for the above question by finding the mass of sphere.

Let suppose the first mass ${m}_{1},$is and the other mass will be ${m}_{2}=5-{m}_{1},$

According to Newton’s law of universal gravitation, we have

${F}_{g}=G\frac{{m}_{1}.{m}_{2}}{{r}^{2}}\phantom{\rule{0ex}{0ex}}1×{10}^{-8}=6.67×{10}^{-11}×\frac{{m}_{1}.\left(5-{m}_{1}\right)}{{0.2}^{2}}..............\left(\because {m}_{2}=5-{m}_{1}\right)\phantom{\rule{0ex}{0ex}}{m}_{1}.\left(5-{m}_{1}\right)=\frac{0.04×{10}^{-8}}{{10}^{-11}×6.67}\phantom{\rule{0ex}{0ex}}{m}_{1}.\left(5-{m}_{1}\right)=5.99\approx 6\phantom{\rule{0ex}{0ex}}{{m}_{1}}^{2}-5{m}_{1}+6=0$

On simplifying and solving, we get,

${m}_{1}=3.00\text{kg}\phantom{\rule{0ex}{0ex}}{m}_{2}=5-{m}_{1}=5-3.00=2.00\text{kg}$

Hence, the masses of objects are ${m}_{1}=3.00kg$ and ${m}_{2}=2.00kg$.