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 r0, G and a dimensionless constant. ii) Use the method of dimensions to find the resulting formula for t.
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 r0, G and a dimensionless constant. ii) Use the method of dimensions to find the resulting formula for t.
The magnitude of the force of gravitational attraction, F, between two objects of mass m1 and m2 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 r0, 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, p0, of the star is used as one of the variables.
G’s dimensions should be determined. A model is proposed in which a star’s lifetime, t, is determined by the product of powers of its mass, m, its initial radius, r0, G, and a dimensionless constant. ii) Find the resulting formula for t using the method of dimensions.
G’s dimensions should be determined. A model is proposed in which a star’s lifetime, t, is determined by the product of powers of its mass, m, its initial radius, r0, G, and a dimensionless constant. ii) Find the resulting formula for t using the method of dimensions.
The magnitude of the gravitational attraction force, F, between two masses m1 and m2 separated by d is given by
