Book edition 9th Edition

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

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Two objects attract each other with a gravitational force of a magnitude $1.00 \times 10^{- 8} N$ 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 $m_{1} = 3.00 k g$ and $m_{2} = 2.00 k g$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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, $G = 6.674 \times 10^{- 11} N \cdot m^{2} {/kg}^{2}$ 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: $F_{g} = 1.00 \times 10^{- 8} N$

Distance between two objects: $r = 20 cm = 0.2 m$

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

$F_{g} = G \frac{m_{1} . m_{2}}{r^{2}} 1 \times 10^{- 8} = 6.67 \times 10^{- 11} \times \frac{m_{1} . (5 - m_{1})}{{0.2}^{2}} . . . . . . . . . . . . . . (∵ m_{2} = 5 - m_{1}) m_{1} . (5 - m_{1}) = \frac{0.04 \times 10^{- 8}}{10^{- 11} \times 6.67} m_{1} . (5 - m_{1}) = 5.99 \approx 6 {m_{1}}^{2} - 5 m_{1} + 6 = 0$

On simplifying and solving, we get,

$m_{1} = 3.00 kg m_{2} = 5 - m_{1} = 5 - 3.00 = 2.00 kg$

Hence, the masses of objects are $m_{1} = 3.00 k g$ and $m_{2} = 2.00 k g$ .

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Physics For Scientists & Engineers

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Short Answer

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

Step by Step Solution

Step 1: Newton’s Law

Step 2: Given

Step 3: Find the masses

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Physics For Scientists & Engineers

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Short Answer

Two objects attract each other with a gravitational force of a magnitude 1.00×10-8 Nwhen separated by 20.0 cm. If the total mass of the two objects is 5.00 kg, what is the mass of each?

Step by Step Solution

Step 1: Newton’s Law

Step 2: Given

Step 3: Find the masses

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