Background: Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x ≤ R from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius r ≤ x; there is no net gravitational force from the mass in the spherical shell with r > x.
Part A. Find an expression for the gravitational force on the particle, assuming the object has uniform density.
Express your answer in terms of the variables x, R, m, M, and appropriate constants.
- Andrew SmithLv 71 month ago
if the density of the planet is d the mass is M= 4/3 pi() r^3 d
F = GMm/ r^2 = G * 4/3 pi() r^3 m / r^2 = ( 4/3 pi() G) r m