Problem 3.1: If the Universal Law of Gravitation was a 1/r³ force instead of a 1/r² force, would it still be possible to treat the mass of a sphere as concentrated at its center? [Solution]

Problem 3.2: Show that the gravitational force is independent of the path taken by evaluating some line integrals explicitly. Take a 10 kilogram mass at (1, 0) and calculate the work done to move a one kilogram mass from (2, 0) to the origin. Take one path as being directly along the x-axis and the other taking a quarter-circle path from (2, 0) to (1, 1), and then a straight path from (1, 1) to (1, 0). [Solution]

Problem 3.3: What is the gravitational potential energy of a 10 kilogram mass which is 10 meters away from a 100 kilogram beam of length 10 meters as shown in the figure? [Solution]

Problem 3.4: Determine the magnitude and direction of the force for the set-up described in the previous problem. [Solution]

Problem 3.5: Show that the gravitational force on a point P inside a spherical shell is zero by the following method: 1) pick a point P; 2) draw two lines through P which intersect the edges of a circle representing the spherical shell--in fact, in three dimensions these lines will makes two cones with their base as pieces of the shell; 3)show that the force from each piece of mass at the ends of the cones cancels. [Solution]