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rajan jha Grade: 12
        

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 

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

 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

6 years ago
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