Question: 1. The constant of gravitation G is defined by

F = G mM F = G m₁m₂
         r²             r²

Where F is the gravitational force between two masses m1 and m2 whose centers of mass are a distance r apart. Find the dimensions of G and its units in both SI and Imperial units

2. Assuming the period of oscillation of a simple pendulum τ to depend on the mass of the object, the length of the pendulum l, and the acceleration due to gravity g, use the theory of dimensional analysis to show that the mass of the object is not, in fact, relevant. Then find a suitable expression for the period of oscillation in terms of the other variables.