A uniform solid disc of mass and radius is to rotate about an axis perpendicular to…
PHYSICS · Subjective · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform solid disc of mass M and radius R is to rotate about an axis perpendicular to its plane passing through its centre. A circular hole of radius 2R is drilled completely through the disc such that the centre of the hole is on a radius of the original disc at a distance 2R from the centre.
(i) Write the expression for the moment of inertia of the original complete disc about the given axis.
(ii) Treating the removed portion as a smaller uniform disc, derive an expression for the moment of inertia of that removed part about the same axis.
(iii) Hence obtain the moment of inertia of the remaining body (the disc with an eccentric hole).
(iv) State, with both numerical result and qualitative reasoning, whether the drilling operation has increased or decreased the moment of inertia compared with the solid disc.