The magnitude of the force of gravitational attraction, F, between two objects of mass m_{1} and m_{2} at a distance d apart is given by

where G is the universal constant of gravitation.

i) Find the dimensions of G. An astronomer proposes a model in which the lifetime, t, of a star depends on a product of powers of its mass, m, its initial radius r_{0}, G and a dimensionless constant. ii) Use the method of dimensions to find the resulting formula for t. Observation shows that the larger the initial radius the longer the lifetime of the star, but that the larger the mass the shorter the lifetime of the star.

iii) Is the model consistent with these observations?

iv) Show that the model can be expressed more simply if the initial density, p_{0}, of the star is used as one of the variables.