Question

The force F of attraction between two bodies varies jointly as the weights of the two bodies and inversely as the square of the distance d between them. Express this fact as a variation using c as a constant. Use M1 and M2 for the weights of the two bodies.

Answer 1

We have that F is proportional to m1. Hence, we have that F=m1*c when we change the first mass. We also have that F=m2*c when we only change the 2nd mass. Since F scales inversely with the square of the distance, we have that $F= \frac{c}{d^2}$. Combining all of the facts above, we get that F=c*$\frac{m_1 m_2}{d^2}$ where c is a constant.