The mass M and moment of inertia C of a thick shell of uniform density p, with internal radius r and exter- nal radius Rare given by M={mp(R° – r°) C=mp(R$ – r°) 8 The Earth has an internal structure consisting of con- centric spherical shells. A simple model with uniform density in each shell is given in the following figure. Density (kg m 3) Radius Layer (km) 6370 upper mantle 3300 5700 lower mantle 5000 3480 outer core 11000 1220 inner core 13000 (a) Compute the mass and moment of inertia of each spherical shell. (b) Compute the total mass and total moment of inertia of the Earth. (c) If the moment of inertia can be written C= kMR?, where M is Earth's mass and Rits radius, what is the value of k? (d) What would the value of k be if the density were uniform throughout the Earth?

The mass M and moment of inertia C of a thick shell of uniform density p, with internal radius r and exter- nal radius Rare given by M={mp(R° – r°) C=mp(R$ – r°) 8 The Earth has an internal structure consisting of con- centric spherical shells. A simple model with uniform density in each shell is given in the following figure. Density (kg m 3) Radius Layer (km) 6370 upper mantle 3300 5700 lower mantle 5000 3480 outer core 11000 1220 inner core 13000 (a) Compute the mass and moment of inertia of each spherical shell. (b) Compute the total mass and total moment of inertia of the Earth. (c) If the moment of inertia can be written C= kMR?, where M is Earth's mass and Rits radius, what is the value of k? (d) What would the value of k be if the density were uniform throughout the Earth?