A) \[{{I}_{A}}={{I}_{B}}\]
B) \[{{I}_{A}}>{{I}_{B}}\]
C) \[{{I}_{A}}<{{I}_{B}}\]
D) \[\frac{{{I}_{A}}}{{{I}_{B}}}=\frac{{{d}_{A}}}{{{d}_{B}}}\]
Correct Answer: C
Solution :
Let same mass and same outer radii of solid Sphere and hollow sphere are M and R respectively. The moment of inertia of solid sphere A about its diameter \[{{I}_{A}}=\frac{2}{5}M{{R}^{2}}\] ...(i) Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter \[{{I}_{B}}=\frac{2}{3}M{{R}^{2}}\] ...(ii) It is clear from Eqs, (i) and (ii),\[{{I}_{A}}<{{I}_{B}}\]is. where\[{{d}_{A}}\]and\[{{d}_{B}}\]are their densities.
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