Question

If `F=(GMm)/d^2`, then `d=`?

Answer 1

`d=sqrt((GMm)/F)`

Explanation:

Given,

`F=(GMm)/d^2`

Multiply both sides by `d^2`.

`Fcolor(red)(*d^2)=(GMm)/d^2color(red)(*d^2)`

Simplifying,

`F*d^2=(GMm)/color(red)cancelcolor(black)(d^2)*color(red)cancelcolor(black)(d^2)`

`F*d^2=GMm`

Divide both sides by `F`.

`color(red)((color(black)(F*d^2))/F)=color(red)((color(black)(GMm))/F)`

Simplifying,

`(color(red)cancelcolor(black)F*d^2)/color(red)cancelcolor(black)F=(GMm)/F`

`d^2=(GMm)/F`

Take the square root of both sides.

`color(red)(sqrt(color(black)(d^2)))=color(red)(sqrt(color(black)((GMm)/F)))`

Simplifying,

`d=color(green)(|bar(ul(color(white)(a/a)color(black)(sqrt((GMm)/F))color(white)(a/a)|)))`