Can I get the solution for these Engineering physics problems? Subject is Classical Mechanics.

Textbook (required): Classical Dynamics of Particles and Systems 5th Ed., by S.T. Thornton and J.B. Marion, Cengage Learning 2012.

1) If the gravitational field vector is independent of the radial distance within a massive sphere, find the function describing the density, p(r), of the sphere. 2) Find an expression for the minimum velocity a particle must have at the surface of the earth to escape the earth's gravitational field. Obtain a numerical value for your result. 3) An object is dropped into a straight frictionless tube that fills a hole dug between two points on the surface of the earth. Neglecting rotational effects, show that the object's motion is simple harmonic. b. Calculate the period of harmonic motion. 4) Show that the gravitational self-energy of a uniform sphere of mass M and radius R is: U = - 3 GM2 75 R 5) How good is the local gravity approximation? a. Taylor expand the universal gravity expression about a radius equal to the earth's mean radius. Use h to represent the height above the earth's surface (which is small relative to the mean radius of the earth). Show the first 2 terms in the expansion. b. Now use only the first term in the expansion to calculate a numerical value of g, and compare with the expected result, g = 9.8m/s2. c. Now use the second term in the expansion to estimate how much your weight changes when flying in an airplane 4 km above the earth's surface