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) |

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) |

1 Answer

127 votes

**(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

MI of this segment about

MI of the quadrant about

127 votes

127