Solve for m₁ f=(gm_1m_2)/(r^2)

$f = \frac{g m_{1} m_{2}}{r^{2}}$

Step 1

Rewrite the equation as $\frac{g m_{1} m_{2}}{r^{2}} = f$ .

$\frac{g m_{1} m_{2}}{r^{2}} = f$

Step 2

Multiply both sides by $r^{2}$ .

$\frac{g m_{1} m_{2}}{r^{2}} r^{2} = f r^{2}$

Step 3

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{g m_{1} m_{2}}{r^{2}} r^{2} = f r^{2}$

Rewrite the expression.

$g m_{1} m_{2} = f r^{2}$

Step 4

Divide each term in $g m_{1} m_{2} = f r^{2}$ by $g m_{2}$ and simplify.

Divide each term in $g m_{1} m_{2} = f r^{2}$ by $g m_{2}$ .

$\frac{g m_{1} m_{2}}{g m_{2}} = \frac{f r^{2}}{g m_{2}}$

Simplify the left side.

Cancel the common factor of $g$ .

Cancel the common factor.

$\frac{g m_{1} m_{2}}{g m_{2}} = \frac{f r^{2}}{g m_{2}}$

Rewrite the expression.

$\frac{m_{1} m_{2}}{m_{2}} = \frac{f r^{2}}{g m_{2}}$

Cancel the common factor of $m_{2}$ .

Cancel the common factor.

$\frac{m_{1} m_{2}}{m_{2}} = \frac{f r^{2}}{g m_{2}}$

Divide $m_{1}$ by $1$ .

$m_{1} = \frac{f r^{2}}{g m_{2}}$