Is it true that if the distance between two objects is doubled, then the gravitational force between them is reduced to $1 / 8 th$ of the original value of force?

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True

False

answer is B.

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Detailed Solution

The above statement is False.
By the universal law of gravitation, we know that the gravitational force between two objects is inversely proportional to the square of the distance between them.
The gravitational attraction between two particles of masses

m

and

M

is given by

F = GmM / r^{2}

Where

r

is the distance between them.
When the distance is doubled, the gravitational force of attraction between them will be

F' = GmM / {(r')}^{2}

Where

r' = 2 r

\Rightarrow F' = GmM / ({2 r)}^{2}

\Rightarrow F' = \frac{1}{4} \frac{GmM}{r^{2}}

\Rightarrow F' = \frac{1}{4} F

Therefore, if the distance between two objects is doubled, then the gravitational force between them is reduced to

1 / 4 th

of the original value of force.
The correct statement would be that if the distance between two objects is doubled, then the gravitational force between them is reduced to