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

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Answer 1 · 2016-06-09T22:16:22

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

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)|)))#