PHYS 21 Lecture 17:

Consider a sphere of radius R=5.00cm.
(a) What is the density of the sphere if its mass is 2.55kg. in1kg/m 3

(b) Suppose instead that one-half the volume of the sphere has adensity of 2.70x103kg/m 3, 0.125 times the volume of the sphere hasa density of 7.80x103kg/m 3, and 0.375 times the volume of thesphere has a density of 11.3x103kg/m 3, what is average density ofthe sphere? in 2kg/m 3

(c) Let's consider another variation to this problem. Suppose thatone-half the mass of the sphere has a density of 2.70x103kg/m 3,0.125 times the mass of the sphere has a density of 7.80x103kg/m 3,and 0.375 times the mass of the sphere has a density of11.3x103kg/m 3, what is average density of the sphere? in 3kg/m3

A sphere rests on a table. The sphere has a mass density ? = 1.0 x 10^3 kg/m^3 and radius R = 1.05 m. The height of the table is h = 1.10 m. Calculate the potential energy. (Make the potential energy be zero if the ball rests on the floor.)

The moment of inertia of the sphere depicted in A (mass M, radius R) is 

For a sphere with a constant density ρ this can be expressed in spherical coordinates:

Show that the Moment of Inertia I of an isotropic sphere is: