Question

From a complete ring of mass M and radius R a 30degree arc is removed. The moment of inertia of the complete ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is

1)9/12 MR2

2)11/12 MR2

3)11.3/12 MR2

4)MR2

Answer 1

mass of arc removed
M/2π × π/6 = M/12
remaining mass of ring (M-M/12) = 11/12 M
moment of inertia perpendicular to the plane and passing through the axis is
I = 11/12 MR^2