CALC Planets are not uniform inside. Normally, they are densest at the center and have decreasing density outward toward the surface. Model a spherically symmetric planet, with the same radius as the earth, as having a density that decreases linearly with distance from the center. Let the density be 15.0 X 103 kg/m3 at the center and 2.0 X 103 kg/m3 at the surface. What is the acceleration due to gravity at the surface of this planet?

Solution to 81P Step 1 of 4 Introduction The density varies with respect to the radius. The density is maximum in the centre of the planet and minimum at the surface. We need to find the acceleration due to gravity at the surface. The density gradient is given as, Given, Density at the centre= 15.0 X 10 kg/m3 3 Density at the surface=2.0 X 10 kg/m3 6 Radius =6.37x10 m