 If they are discrete masses then simply I do m 1 r 1 square plus m 2 r 2 square but if it is continuous mass the infinite such masses exist small small dm so I can't do summation I have to take help of integral now ok understood all of you understood right so now we are going to take up one by one different different objects and we will apply this popular of integral r square dm fine ok first write down ring how much you put out the axis ok so we are determining about the axis which is passing through the center and perpendicular to the plane like this ok about this axis what is the moment of an axis of this ring is in this one right so this is the small mass let's say this is the small mass dm what is a perpendicular is integral of perpendicular which is r square into dm same only so r square will come out of integral this will become r square integral of dm integral dm is what some of all passing through the center and perpendicular to the plane about the natural axis we got it how much it is if mass if an entire if an entire mass is located a distance r then the moment of inertia is m r square simply if the perpendicular distance of all is same so here as you mean masses are equal then only this end need not be equal to that end so we have got the moment of inertia about the axis passing through the center a ring of radius is small r small r with dm and your small r will change from 0 to capital r now you are basically integrating dm with i d i is for the so r square dm this is the moment of in terms of d r now this is mass per unit and the same thing center of mass also for the same it is done by r square into this like this right escape this if you think that if you have any doubts ask this will go for mass of the same it is so difficulty and this difficulty will work this will not going to help you anyway if you are not doing this this will not improve isn't it very straight forward and in class 12 same mass could become charge so you have to find charge per unit area into the area of the strip it will be again total charge q will be dq small charge in the strip ok so you just need to learn once and then replicate minimum charge it is not 0 why? you have to go over to each other fine so for solid cylinder also the moment of inertia ok