$\"\"$

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Force $\"\"$ exerted by a body of mass $\"\"$ on a body of mass $\"\"$ is $\"\"$ .

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Where $\"\"$ is the gravitational constant and $\"\"$ is the distance between the bodies.

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(a)

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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From the above expression, negative sign indicates that force is decreasing as distance $\"\"$ increases.

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$\"\"$

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(b)

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Earth attracts object an object with a force that decreases at a rate of $\"\"$ N/Km when $\"\"$ Km.

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That is $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in above expression.

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$\"\"$

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Substitute $\"\"$ in above expression.

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Change of force when $\"\"$ :

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Consider $\"\"$ .

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Substitute $\"\"$ in above expression.

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$\"\"$

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$\"\"$ N/Km.

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ N/Km.