From a uniform disc of Radius R and mass 9kg, a small disc of radius r/3 is removed from disc - Physics - System Of Particles And Rotational Motion

Question

From a uniform disc of Radius R and mass 9kg, a small disc of
radius r/3 is removed from disc concentrically What will be the
moment of inertia of remaining disc, passing through the centre and
perpendicular to its plane ?

Neha Gupta · Accepted Answer

Initially mass of the disc is m and radisu of the disc is r
Initial moment of inertia i = 12mr2When radius r/3 part is cut from the disc and is taken out
Mass of the this part is given by:πr2 has mass = mπ(r/3)2 has mass = mπr2π(r/3)2  = m9Mass of the remaining part is m -m9 = m10Moment of inertia of the remainf part abou the centre of the  disc and perpendicular to the plane is:I' = 12m10r2I' = I10

From a uniform disc of Radius R and mass 9kg, a small disc of radius r/3 is removed from disc concentrically. What will be the moment of inertia of remaining disc, passing through the centre and perpendicular to its plane ?