86.2 Gravitational force of a uniform sphere on a particle Exercise 3: P240-241 (a)a point mass m located outside the sphere; (b)a point mass m located within the volume enclosed by the sphere itself. Solution: (a) F_GmM M 4m3/3 (b) 4丌R/3R gm(rM/R) GmM 86.2 Gravitational force of a uniform sphere on a particle Exercise 4: A spherical hollow is made in a lead sphere of radius R, such that its surface touches the outside surface of the lead sphere and passes through its center. The mass of the sphere before hollowing was m. what is the attracting force between a small sphere of mass m and the hollowing sphere. 1010 Exercise 3: P240~241 Solution: (a) A point mass m located outside the sphere; (b) A point mass m located within the volume enclosed by the sphere itself. (a) 2 r GmM F = (b) r R GmM r Gm r M R F 3 2 3 3 ( ) = = 3 3 3 3 4 3 4 3 R r R r = π π r M r M §6.2 Gravitational force of a uniform sphere on a particle R r F F ∝ r 2 F∝1/r 2 R GmM §6.2 Gravitational force of a uniform sphere on a particle Exercise 4: A spherical hollow is made in a lead sphere of radius R, such that its surface touches the outside surface of the lead sphere and passes through its center. The mass of the sphere before hollowing was M. What is the attracting force between a small sphere of mass m and the hollowing sphere. d R m