wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Calculate the moment of Inertia of uniform solid sphere of mass M and Radius R, about its diameter


A

23MR2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

25MR2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

53MR2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

52MR2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

25MR2


Draw two spheres of radii x and (x+dx), concentric with the given solid sphere. The thin spherical shell trapped between these spheres may be treated as a hollow sphere of radius x.

Mass per volume of the solid sphere = 3M4πR3

The thin hollow sphere considered above has a surface area 4πx2 and thickness dx. Its volume is 4πx2 dx and hence its mass is

= (3M4πR3).(4πx2 dx)

= 3Mx2 dxR3

Its moment of Inertia about diameter O is therefore,

dI = 23[3Mx2 dxR3].x2 = 2Mx4 dxR3

As x increases from 0 to R, the shell covers the whole solid sphere, therefore,

I = R02MR3x4dx = 25MR2


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Moment of Inertia of Solid Bodies
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon