Question

Rearrange the following equation to make G the subject where r>0 and M>0: 8pi^2/G^3M = T^2/r^3?

Answer 1

`G=root(3)((8pi^2r^3)/(MT^2))`

Explanation:

`"one way is to use the method of "color(blue)"cross-multiplication"`

`• " given "a/b=c/drArrad=bc`

`(8pi^2)/(G^3M)=(T^2)/(r^3)`

`rArrG^3MT^2=8pi^2r^3`

`"divide both sides by "MT^2`

`(G^3cancel(MT^2))/cancel(MT^2)=(8pi^2r^3)/(MT^2)`

`rArrG^3=(8pi^2r^3)/(MT^2)`

`color(blue)"take the cube root of both sides"`

`root(3)(G^3)=root(3)((8pi^2r^3)/(MT^2))`

`rArrG=root(3)((8pi^2r^3)/(MT^2))to(T!=0)`