A) \[{{l}_{A}}={{l}_{B}}\]
B) \[{{l}_{A}}>{{l}_{B}}\]
C) \[{{l}_{A}}<{{l}_{B}}\]
D) \[\frac{{{l}_{A}}}{{{l}_{B}}}\,=\frac{{{d}_{A}}}{{{d}_{B}}}\] where\[{{d}_{A}}\]and\[{{d}_{B}}\]are their densities.
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 \[{{l}_{A}}=\frac{2}{5}\,M{{R}^{2}}\] ...(i) Similarly, the moment of inertia of hollow sphere (spherical shell) B about its diameter \[{{l}_{B}}=\frac{2}{3}\,M{{R}^{2}}\] ...(ii) It is clear from Eqs. (i) and (ii), \[{{l}_{A}}<{{l}_{B}}\]. Alternatively We can say that the object which has mass at greater distance will have higher moment of inertia as \[l=m{{r}^{2}}\]. So, hollow sphere (B) has large\[l\], because it has mass only on its circumference.
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