One of the first things you learn in physics class is the

Chapter 7, Problem 68P

(choose chapter or problem)

Problem 68P

One of the first things you learn in physics class is the law of universal gravitation,  where F is the attractive force between two bodies, m1, and m2 are masses of the two bodies, r is the distance between the two bodies, and G is the universal gravitational constant equal to (6.67428 ± 0.00067) × 10 −11 [the units of G are not given here], (a) Calculate the SI units of G. For consistency, give your answer in terms of kg, m, and s. (b) Suppose you don’t remember the law of universal gravitation, but you are clever enough to know that F is a function of G, m1,m2, and r. Use dimensional analysis and the method of repeating variables (show all your work) to generate a nondimensional expression for F = F(G, m1, m2, r). Give your answer as Π1 = function of (Π2, Π 3,…). (c) Dimensional analysis cannot yield the exact form of the function. However, compare your result to the law of universal gravitation to find the form of the function (e.g., Π1, = Π 22 or some other functional form).