how to find the moment of inertia of a disc of variable densityfor ex -find the MOI wrt Centre of a disk of surface density which varies as (A + Br) where r is distance from centre Total radius - R?

Dear Aakash

I=∫(dm)r²

you have to take an element and find dm for that

take ring of width dr at a distance r from the centre

area of elemental ring=2∏rxdr

mass of this ring= dm= (A+Br)2∏rxdr

I=∫(A+Br)2∏r³ dr limits from 0 to R

just intrgrate

I=2∏(AR⁴/4 + BR⁵/5)

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

take elemental ring of r & thickness dr ...

mass of this ring is dm = (A+Br)2pirdr

moment of inertia = dmr²

now integrate this , take limit from 0 to R ...

this will give the total moment of inertia .....