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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

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 

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

 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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