Moment Of Inertia

As stated in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), moment of inertia measures a body's resistance to angular acceleration and depends on how the mass is distributed relative to the rotation axis. The farther the mass lies from the axis, the larger the moment of inertia, since each mass element contributes in proportion to the square of its distance. For a uniform thin rod rotating about a perpendicular axis through its centre, the standard result is I_centre = ML²/12. To find the moment of inertia about a parallel axis through one end, we apply the parallel axis theorem, I = I_centre + Md², where d = L/2 is the distance between the central axis and the end axis. Substituting gives I = ML²/12 + M(L/2)² = ML²/12 + ML²/4 = ML²/12 + 3ML²/12 = 4ML²/12 = ML²/3. The option ML²/12 is wrong because it is the value about the central axis, not the end. The option ML²/2 overestimates the distribution and is not derived from any valid axis position. The option ML²/6 does not follow from correct application of the parallel axis theorem. A dimensional check confirms the result has units of mass times length squared, consistent with moment of inertia, and the end value is correctly larger than the central value because the mass is, on average, farther from the end axis.