Guest

moment of inertia of a hollow sphere of mass M and inner radius R and outer radius 2R having uniform mass distribution about diameter axis is

moment of inertia of a hollow sphere of mass M and inner radius R and outer radius 2R having uniform mass distribution about diameter axis is

Grade:12

1 Answers

Arun
25750 Points
6 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 

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free