Question

The gravitational force produced between any two

objects kept at 2.5*10^km apart is 580N. at what distance
should they be kept so that the gravitational force becomes
half?​

Answer 1

The two objects should be kept at a distance of
`3.535* 10^(4)` kilometers.

Step-by-step explanation:

From Newton's Law of Gravitation, gravitational force (
`F`), measured in newtons, between two objects is inversely proportional to the square of distance (
`r`), measured in meters. That is:

`F \propto (1)/(r^(2))` (1)

`F = (k)/(r^(2))` (2)

Where
`k` is the proportionality ratio, measured in newtons-square meter.

Now we eliminate the proportionality by constructing the following relationship:

`(F_(2))/(F_(1)) = \left((r_(1))/(r_(2))\right)^(2)` (3)

If we know that
`(F_(2))/(F_(1)) = (1)/(2)` and
`r_(1) = 2.5* 10^(7)\,m`, then the distance between the two objects so that gravitational force becomes half is:

`(1)/(2) = ((2.5* 10^(7)\,m)^(2))/(r_(2)^(2))`

`r_(2)^(2) = 1.25* 10^(15)\,m^(2)`

`r_(2) = 3.535* 10^(7)\,m`

`r_(2) = 3.535* 10^(4)\,km`

The two objects should be kept at a distance of
`3.535* 10^(4)` kilometers.