Question

Solve for the variable "d" in the following equation. 5E2%7D" id="TexFormula1" title="F=\frac{Gm_1 m_2}{d^2}" alt="F=\frac{Gm_1 m_2}{d^2}" align="absmiddle" class="latex-formula">

Answer 1

Since "m1" and "m2" represent different masses, we can change them to different letters. This will make it easier to solve.

m1 = m

m2 = n

F = G*m1*m2/d^2 → F = Gmn/d^2

Steps to solve for d:

F = Gmn/d^2

~Multiply d^2 to both sides

d^2 * F = d^2 * Gmn/d^2

~Simplify

d^2 * F = Gmn

~Divide F to both sides

d^2*F/F= Gmn/F

~Simplify

d^2 = Gmn/F

~Take the square root of both sides

√d^2 = ±√Gmn/F

~Simplify

d = ±√Gmn/F

Since we are done solving for d, we can input "m1" and "m2" to replace "m" and "n".

d = ±√Gmn/F → d = ±√G*m1*m2/F

Therefore, the answer is [ d = ±√G*m1*m2/F ]

Best of Luck!

Answer 2

$F = \frac{Gm_{1}m_{2} }{d^{2} }$

F x $d^{2}$ = G$m_{1}m_{2}$

$d^{2}$ = $\frac{Gm_{1}m_{2}}{F}$

d = ±$\sqrt{\frac{Gm_{1}m_{2}}{F} }$