Thread: gravitation question

a solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F1 on a particle placed at a distance 3R from the centre of the sphere a spherical cavity of radius r/2 is now made in the sphere .the sphere with cavity now applies a gravitational force F2 on the same particle.the ratio F1/F2 is

Originally Posted by prasum

a solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F1 on a particle placed at a distance 3R from the centre of the sphere a spherical cavity of radius r/2 is now made in the sphere .the sphere with cavity now applies a gravitational force F2 on the same particle.the ratio F1/F2 is

The problem is spherically symmetric so no problems with using the usual force law for gravitation:

where M is the mass of the sphere and m is the mass of the object.

To evaluate this we need the mass of the whole sphere. It has a constant mass density, call it . Then we know that


So


Now your turn. Find the mass of the removed section. Notice that the problem is still spherically symmetric so that


where is the removed mass.

Now form the fraction and you will find that practically everything cancels out.

-Dan