Question

A famous instance of variation is Newton’s Law of Gravity. It states that the magnitude of the Force, F, of gravitational attraction between two masses, m1 and m2, varies directly with the product of the masses and inversely with the square of the distance, r, between them. Write a variation equation relating F, m1, m2, and r.

Answer 1

$\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ F=\cfrac{k(m_1\cdot m_2)}{r^2}\leftarrow \textit{F varies directly with a product and inversely with }r^2$