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 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

That's Newton's Law of Gravitation. Since it varies directly with M1 and M2 and inversely with the square of the distance, we have: \[ F \alpha \frac{M_1 M_2}{d^2} \]Where alpha means that Force is proportional to that. But we need a constant, known as proportionality constant, to make the equation true. So: \[ F = c \frac{M_1 M_2}{d^2} \]