physics

F=G.M.m/r^2
25=[6.67E-11*2*M] / .36^2
Solve for M:
25 = 1.02932×10^-9 M

25 = 1.02932×10^-9 M is equivalent to 1.02932×10^-9 M = 25:
1.02932×10^-9 M = 25

Divide both sides of 1.02932×10^-9 M = 25 by 1.02932×10^-9:
(1.02932×10^-9 M)/(1.02932×10^-9) = 25/(1.02932×10^-9)

(1.02932×10^-9)/(1.02932×10^-9) = 1:
M = 25/(1.02932×10^-9)

25/(1.02932×10^-9)  =  2.42879×10^10:
Answer: |  M = 2.42879×10^10 Kilograms--mass of each body.

Two spherical objects have equal masses and experience a gravitational force of 25 N towards one another. Their centers are 36cm apart. Determine each of their masses.

Newton:

\(\begin{array}{rcll} F &=& G \cdot \frac{m_1\cdot m_2}{r^2} \\ \end{array}\)

where:

   \(\begin{array}{rl} F & \text{is the force between the masses} \\ G & \text{is the gravitational constant } (6.674\cdot 10^{-11}\ N\cdot (\frac{m}{kg})^2) \\ m_1 & \text{is the first mass} \\ m_2 & \text{is the second mass} \\ r & \text{is the distance between the centers of the masses} \\ \end{array} \)

\(\begin{array}{rcll} m_1 = m_2 &=& m \\ F &=& G \cdot \frac{m\cdot m}{r^2} \\ F &=& G \cdot \frac{m^2}{r^2} \qquad & | \qquad \cdot r^2\\ F \cdot r^2&=& G \cdot m^2 \qquad & | \qquad :G\\ \frac{F}{G} \cdot r^2&=& m^2 \\ m^2 &=& r^2 \cdot \frac{F}{G} \qquad & | \qquad \sqrt{}\\ \mathbf{m} &\mathbf{=}& \mathbf{r \cdot \sqrt{\frac{F}{G}} }\\\\ \end{array}\)

\(\begin{array}{rcll} F &=& 25\ N \\ G &=& 6.674\cdot 10^{-11}\ N\cdot (\frac{m}{kg})^2 \\ r &=& 0.36\ m\\\\ m &=& r \cdot \sqrt{\frac{F}{G}} \\ m &=& 0.36\ m \cdot \sqrt{\frac{25\ \not{N} }{6.674\cdot 10^{-11}\ \not{N}\cdot (\frac{m}{kg})^2}} \\ m &=& 0.36\ m \cdot \sqrt{\frac{25}{6.674\cdot 10^{-11}\cdot (\frac{m}{kg})^2}} \\ m &=& 0.36\ m \cdot 5 \cdot \frac{kg}{m} \cdot \sqrt{ \frac{1}{6.674\cdot 10^{-11} } } \\ m &=& 1.8\cdot \sqrt{ \frac{1}{6.674\cdot 10^{-11} } }\ kg \\ m &=& 1.8\cdot \sqrt{ \frac{10^{11}}{6.674 } }\ kg \\ m &=& 1.8\cdot \sqrt{ \frac{10^{10}\cdot 10 }{6.674 } }\ kg \\ m &=& 1.8\cdot 10^5 \sqrt{ \frac{ 10 }{6.674 } }\ kg \\ m &=& 1.8\cdot 10^5 \cdot 1.22407181693\ kg \\ m &=& 2.20332927048\cdot 10^5 \ kg \\ \mathbf{m} &\mathbf{=}& \mathbf{2.20332927048\cdot 10^5 \ kg } \\ \end{array}\)

Their masses are each \(\mathbf{2.20332927048\cdot 10^5 \ kg }\)