Moment Of Inertia Of Standard Bodies

As given in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), the moment of inertia depends on how far each element of mass lies from the rotation axis, with mass located farther out contributing far more because each contribution scales with the square of the distance. For a uniform solid sphere rotating about a diameter the standard result is I = (2/5)MR², while for a thin spherical shell about a diameter it is I = (2/3)MR². Since 2/3 is greater than 2/5, the spherical shell has the larger moment of inertia when the two bodies share the same mass and radius. The physical reason is that the shell concentrates all of its mass at the maximum radial distance R, whereas the solid sphere distributes its mass throughout the interior, placing much of it closer to the axis on average. The option 'The solid sphere' is wrong because its internal mass lowers the average distance from the axis. The option 'Both are equal' ignores the clearly different mass distributions. The option 'It depends on angular velocity' is incorrect because moment of inertia is a purely geometric and mass-distribution property, independent of how fast the body spins. A check confirms that 2/3 MR² exceeds 2/5 MR², so the hollow shell indeed has the greater moment of inertia.