If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force ? Would this be an increase or decrease in the mass ?
As gravitational force is given by: $F=G\frac{m_1m_2}{r^2}$
Here, $G\rightarrow$ gravitational constant
$m_1\rightarrow$ mass of the first object
$m_2\rightarrow$ mass of the second object
$r\rightarrow$ distance between the two objects
If the distance between the two objects is increased by a factor of 5, then the distance between the two objects becomes $5r$. Then, the gravitational force between the objects becomes:
$F=G\frac{m_1m_2}{(5r)^2}$
Or $F=G\frac{m_1m_2}{25r^2}$
Here we find if the distance between the two objects is increased by a factor of 5, then the gravitational force of attraction decreases by 25 times.
Therefore, the mass of one of them should be increased 25 times to maintain the same gravitational force.
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