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The m.i of hollow sphere (mass =M)OF INNER RADIUS r and outer radius 2r ,having material of uniform density,about a diametric axis is
dencity of sphere (d) = M/V
V = 4pi/3 ((2r)3 -r3)=4pi (7r3) /3
d = 3M/4pi(7r3)
now , consider a hollow sphere of thickness dx at a distance x from center..... ( x is in between r to 2r..)
mass of this sphere = dm = d(4pix2dx)
dm= 3Mx2dx/7r3
now moment of inertia of this elemental hollow sphere is dI
dI = 2dmx2 /3 (Isphere (hollow) = 2mr2/3)
dI = (2/7)(M/r3)x4dx
now integrating
I = (2/35)(M/r3)x5 lim r to 2r
I = (62/35)Mr2
approve if u like it
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