# One quarter sector is cut from a uniform circular disc of radius  This sector has mass . It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is a) b) c) d)

## Question ID - 100625 :- One quarter sector is cut from a uniform circular disc of radius  This sector has mass . It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is a) b) c) d)

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(a)

We cannot consider the quadrant as a single mass as the distance of different particles is different from the axis of rotation. So we take the help of calculus. Let us consider a segment as shown in Figure. All masses lying in this segment are at a distance  from the axis and hence considerd as a small differential mass . Let the thickness of the segment be

The mass per unit area of the quadrant =

Area of the segment

Mass of the segment