Parallel Axis Theorem

The parallel axis theorem lets us shift a moment of inertia from an axis through the centre of mass to any parallel axis using $I=I_{cm}+M{d}^2$, where $d$ is the separation between the two axes. For a disc about its central perpendicular axis, $I_{cm}=\frac{1}{2}M{R}^2=\frac{1}{2}(2)(0.5{)}^2=0.25{\text{ kg m}}^2$. The tangent axis lies a distance $d=R=0.5\text{ m}$ from the centre, so the shift term is $M{d}^2=(2)(0.5{)}^2=0.5{\text{ kg m}}^2$. Adding the two contributions, $I=0.25+0.5=0.75{\text{ kg m}}^2$. The value 0.25 kg m${}^2$ forgets the shift term entirely and reports only $I_{cm}$. The value 0.50 kg m${}^2$ keeps only the shift term and drops $I_{cm}$. The value 1.0 kg m${}^2$ wrongly uses $M{R}^2$ for the central disc instead of $\frac{1}{2}M{R}^2$. This is a direct NCERT application of the parallel axis theorem. As a check, the off-centre value must exceed the central value, and $0.75>0.25$ confirms it. The theorem works because shifting the axis introduces an additional contribution equal to treating the entire mass as orbiting the new axis at distance d, which is simply added on top of the body's intrinsic spin about its own centre of mass.