Newtons law of gravity and Coulombs law are both

Chapter 24, Problem 24.83

(choose chapter or problem)

Newtons law of gravity and Coulombs law are both inversesquare laws. Consequently, there should be a Gausss law for gravity. a. The electric field was defined as E u = F u on q /q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g u of a point mass?Write your answer using the unit vector nr, but be careful with signs; the gravitational force between two like masses is attractive, not repulsive. b. What is Gausss law for gravity, the gravitational equivalent of Equation 24.18? Use G for the gravitational flux, g u for the gravitational field, and Min for the enclosed mass. c. A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as r = r011 - r/2R2, where r0 is the density at the center. Determine r0 in terms of M and R. Hint: Divide the planet into infinitesimal shells of thickness dr, then sum (i.e., integrate) their masses. d. Find an expression for the gravitational field strength inside the planet at distance r 6 R.