IB Physics Gravitational fields

A tutorial sheet of questions on Topic D gravitational fields, HL, appears below.

1. Equipotential curves are drawn around a point mass. The difference in potential between the curves is constant. Do the equipotential curves become closer in distance, further in distance or the same separation as the distance from the point mass increases?
2. When the potential is maximum the field strength is zero. True of false?
3. When the field strength is maximum the potential is maximum. True or false?
4. Equal masses are placed at the vertices of an equilateral triangle. Sketch the gravitational field lines around the masses.
5. Explain why gravitational potential is negative in sign.
6. Two equal point masses M are placed a distance d apart. A point mass m is moved from infinity at a constant speed and is placed at the midpoint of the line joining the masses. Find the work done by an external force in moving the mass m from infinity to its final position. Does the work depend on the path taken?
7. A uniform solid sphere has a mass M and radius R. State the gravitational potential and field strength for (a) r >R (b) r < R. Sketch graphs for each case.
8. A uniform spherical shell has a mass M and radius R. State the gravitational potential and field strength for (a) r > R (b) r < R. Sketch graphs for each case.
9. Find the gravitational potential energy of a uniform solid sphere of mass M and radius R.
10. Find the gravitational potential energy of a uniform spherical shell of mass M and radius R.