Sphere Let us find the moment of inertia of a uniform solid sphere of radius a and mass m about an axis (the z-axis) passing through the center. We divide the sphere into thin circular discs, as shown in Figure 8.3.3. The moment of inertia of a representative disc of radius y, from Equation 8.3.7, isy²dm. But dm = pay² dz; hence, 2 4 8 I = py* dã = Enpa – z) dữ = pa 15 wa (8.3.8) The last step in Equation 8.3.8 should be filled in by the student. Because the mass m is given by we have m = na ³ p παρ I₂ = ² ma² for a solid uniform sphere. Clearly also, I₂ = ly = Iz (8.3.9) (8.3.10)

Please obtain the same result as in the book.

Legrende polynomials The amplitude of a stray wave is defined by: SO) =x (21+ 1) exp li8,] sen 8, P(cos 8). INO Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the central potential that performs the scattering. The total cross section is: Show that: 'É4+ 1)sen² 8, .